1. Atomic Structure Atomic Structure
2. Atomic Structure Atom y Each element is composed of smallest particles known as ‘ATOM’. y Atom the name is derived from Greek word Atom means - ‘Not to be cut’. DALTON’S THEORY OF ATOM J. Dalton developed his famous theory of atom in 1803. The main postulates of y Atom was considered as a samllest, dense and hard indivisible particle. y Each element consists of a specific type of atoms. y The properties of elements differ because of difference in kinds of atom contained in them. y This theory provides a satisfactory basis for law of chemical combinaiton. Limitations of Dalton’s Theory y Dalton’s theory fails to explain why atoms of different kinds should differ in valency and mass etc. y The discovery of isobars and isotopes showed that atoms of same elements have different atomic masses (isotopes) and atoms of different kinds may have same atomic masses (isobars). Concept Ladder Atoms is indestructible, i.e., it cannot be created or destroyed. Rack your Brain Why and how do atoms combine together to form compound atoms? Definition Each element is composed of smallest particles called ‘ATOM’. Concept Ladder Democritus was the person who first suggested the existence of ATOM & coined the name ATOMOS means Not to be cut or Indivisible.
3. Atomic Structure y The discovery of various sub-aomic particles like protons, electrons, X-rays etc. during late 19th century lead to idea that the atom was no longer an indivisible and smallest particle of the matter. DISCOVERY OF FUNDAMENTAL PARTICLES y Atom consist of several sub-atomic particles like neutron, proton, electron, neutrino, positron etc. Out of these particles, electron, proton and the neutron are called fundamental subatomic particles. (1) Electron y Electron discovered by J.J. Thomson (1897) and it is negatively charged particle. Cathode Ray Experiment y William Crookes in 1879 studied the electrical discharge in partially evacuated tubes called as cathode ray discharge tube. Concept Ladder R.S. Mullikan measured the charge on an electron by oil drop experiment. The charge on each electron is –1.602 × 10–19 C. Rack your Brain Why, cathode rays do not depend upon the nature of gas or the cathode meterial used in discharge tube? y Discharge tube is made of glass, about 60 cm long containing two thin pieces of metals known as electrodes, sealed in it. This is called crooke’s tube. Negative electrode is called as cathode and positive electrode is called anode.
4. Atomic Structure y When a gas enclosed at low pressure (~10–4 atm) in discharge tube is subjected to a high voltage (~10,000 V), invisible rays originating from the cathode and producing a greenish glow behind the perforated anode on the glass wall coated with phosphorescent material ZnS is observed. These rays Properties y Cathode rays travel in straight line. y Cathode rays produce mechanical effect, as they can rotate the wheel that placed in their path. y Cathode rays consist negatively charged particles called as electron. y Cathode rays travel with high speed. y Cathode rays can cause fluorescence. y Cathoderays heat the object on which they fall due to transfer of kinetic energy to the object. y When cathode rays fall on heavy metals, X-rays produced. y Cathode rays possess ionizing power that is they ionize the gas through which they pass. y The cathode rays produce scintillation on the photographic plates. y They can penetrate through thin metallic sheets. Rack your Brain Why do cathode rays produce fluorescence? Concept Ladder Order of specific charge < < n p e e e e m m m – p e mmass of proton 1837 mass of electron m = = Previous Year’s Question Cathode rays have [AIPMT] (1) Mass only (2) Charge only (3) No mass and charge (4) Mass and charge both
5. Atomic Structure DISCOVERY OF FUNDAMENTAL PARTICLES Charge by mass ratio of Cathode Ray Electron is a low-mass, negatively charged particle. It can easily be swing by passing close to other electron or positive nucleus of an atom. With the help of variation in electric and magnetic fields the ratio was determined. The apparatus is shown below. The charge to mass ratio of the electron is given Charge to mass ratio of electron is given by: e/m = 1.758820 × 1011 C/kg Where; m = mass of electron in kg. e = magnitude of the charge of electron in coulombs. (2) Proton y Proton was discovered by Goldstein and it is positively charged particle. Anode Ray Experiment Canal Ray experiment is the experiment performed by German scientist Eugen Goldstein in 1886 that led to the discovery of the proton. The discovery of proton which happened after the discovery of the electron further strengthened the structure of the atom. In the experiment, Goldstein applied high voltage across a discharge tube which had a perforated cathode. A faint luminous ray was Concept Ladder Anode rays, e/m value is dependent upon the nature of the gas taken in the tube. It is maximum when gas present in the tube is hydrogen. Rack your Brain What were the important conditions maintained in the discharge tube by Goldstein?
6. Atomic Structure seen extending from the holes in the back of the cathode. Properties y Anode rays travel in wtraight line. y Anode rays are material particle. y Anode rays are positively charged. y Anode rays may get swing by external magnetic field. y Anode rays also affect the photographic plate. y e/m ratio of anode rays is lesser than electrons. y These anode rays produce flashes of light on ZnS screen. (3) Neutron y In 1932, Chadwick bombarded Be with a stream of a-particles (He+2). He noticed that penetrating radiations were produced which not affected by magnetic field and electric field. These radiationss consisted of neutral particles, which were called neutrons. Previous Year’s Question The discovery of neutron become very late because [AIPMT] (1) Neutrons are present in nucleus (2) Neutrons are highly unstable particles (3) Neutraons are chargeless (4) Neutrons do not move Concept Ladder Anode rays were observed by E. Goldstein but was named by E. Rutherford.
7. Atomic Structure 4Be9 + 2He4 → 6C12 + 0n1 5B11 + 2He4 → 7N14 + 0n1 y These radiation was made incident on paraffin wax, a hydrocarbon having a relatively high H2 content. y These protons ejected from the paraffin wax (when struck by uncharged radiation) were observed with the help of ionization chamber. y The range of the liberated protons was measured and the interaction between the uncharged radiation and the atoms of several gases was studied by Chadwick. y The neutron is relatively massive but neutral, it is scarcely affected by the cloud of electrons surrounding the nucleus or by the positive electrical barrier of the nucleus it self, thus it can penetrate the nucleus of any element Concept Ladder Neutron is fundamental particle of all the atomic nucleus, except hydrogen or protium.
8. Atomic Structure Particles Symbol Mass Charge Discovered By Electron –1e0 or β 9.1096 × 10–31 kg 0.000548 amu –1.602 × 10–19 Coulombs –4.803 × 10–10 esu J.J. Thompson Stoney Lorentz 1887 Proton 1H1 1.6726 × 10–27 kg 1.00757 amu +1.602 × 10–19 Coulombs + 4.803 × 10–10 esu Goldstein Rutherford 1907 Neutron 0n1 1.6749 × 10–27 kg 1.00893 amu 1 amu ≈ 1.66 × 10–27 kg Neutral 0 James Chadwick 1932 MODELS OF ATOM (1) Thomson’s Model y Thomson was the first proposed a detailed model of atom. y Thomson proposed that an atom consist of a uniform sphere of positive (+ve) charge in which electrons are present at some places. y This model of atom is known as ‘Plum- Pudding model’. Concept Ladder The colloquial nickname ‘plum pudding’ was soon attributed to Thomson’s model as distribution of electrons within its positively charged region of space reminded many scientists of raisins, then called ‘plums’. Rack your Brain What is the name of Thomson’s model?
9. Atomic Structure Limitations of Thomson’s Theory y An importnat drawback of this model is that the mas of the atoms is considered to be evenly spread over that atom. y It is a static model. It does not reflect the movement of electron. (2) Rutherford’s a-Scattering Experiment y Rutherford carried out a-particles scattering experiment by the bombardment of high speed a-particle on thin foil of gold, emitted from radius and gave the following observations, which was based on his experiment. y The angular deflections of scattered a-particles were studied with the help of moving microscope. Concept Ladder The relation between number of deflected particles and deflection angle q is 1 2 4 sin Where, m = deflected particles q = deflection angle Previous Year’s Question The nucleus of atom consists of [AIPMT] (1) Proton and neutron (2) Proton and electron (3) Neutron and electron (4) Proton, neturon and electron
10. Atomic Structure Observations Rutherford execute a number of experiments, involving the scattering of a-particles (He+2) by very thin foil of gold. Observations were: y Most of the a-particles (99%) passes through it, without any deviation or deflection. y Some of the a-particles were deflected through small angles. y Very few a-particles were deflected by large angles and occasionally an a-particle got deflected by 180°. Conclusions y Most of the a-particle (He+2) went straight through metal foil undeflected, it means that there must be very large empty space within atom. y Since few of the a-particles were defelcted from their original path through moderate angle; it was concluded that whole of the positive (+ve) charge is concentrated and the space occupied by this positive charge is very small in the atom. y When a-particles comes closer to this point, they bear a force of repulsion and diverge from their path. Concept Ladder An atom consists of positively charge center which is known as nucleus e– revolves around nucleus (+) like solar system Previous Year’s Question Rutherford experiment prove [AIPMT] (1) Electron (2) Proton (3) Atom (4) Nucleus
11. Atomic Structure y Positively (+ve) charged heavy mass which occupies only a small volume in an atom is known as nucleus. Nucleus is supposed to be present at the centre of atom. y A very few of the a-particles (He+2) suffered strong diversion on even returned on their path indicating that nucleus is rigid and a-particles (He+2) recoil due to direct collision with heavy positively charged mass. y As atomic number increases, the number of protons increases which increases the repulstuion and so deflection angle q increases. y Atom has two part (1) Nuclear part (2) Extra nuclear part ↓ ↓ Mass Size, volume Size of nucleus = 10–13 cm or 10–15 m = 1 fermi Size of atom = 10–8 cm or 10–10 m = 1 Å = = = = –13 –5N N –8 A A r D 10 10 r D 10 y Density of nucleus = + 1017 kg /m3 Limitations of Rutherford’s a-scattering experiment y It does not obey Maxwell theory of electrodynamics. Charge particle in attractive field revolves to emits its energy. So It’s loop is reduced and collide with nucleus. Concept Ladder y Mass Number (A) = Number of Protons (Z) + Number of Neutrons (n) y Number of Neutrons (n) = Mass Number (A) – Number of Protons (Z) Concept Ladder ( )α 1/3 nR A A = mass no Rn= R0 {A} 1/3 = = × 0 –13 R 1.33 fermi 1.33 10 cm ( )=3 3 n 0R R A Rn = Radius of nucleus R0 = constant Rack your Brain Why was Rutherford’s model rejected?
12. Atomic Structure y But in reality discontinuous spectrum occur. ATOMIC NUMBER AND MASS NUMBER (1) Atomic Number (Z) y It is always equal to number of protons present in the nucleus of the atom of the element. It also represents the number of electrons in the neutral atom. Ex: Number of protons in K is 19, so its atomic number (Z) = 19. (2) Mass Number (A) y The neutrons and protons present in nucleus of an atom are collectively known as nucleons. Atomic Weight y It is the average of average of weights of the all isotopes of that element. y An element have two isotopes Z1 and Z2, that of isotopes are W1 and W2 and their % of occurance in nature are X1 and X2 respectively then the average atomic weight of element is — avg. wt W X W X X X 1 1 2 2 1 2 Previous Year’s Question The number of electrons and neurons of an element is 18 and 20 respectively. Its mass number is : [AIPMT] (1) 17 (2) 37 (3) 2 (4) 38 Concept Ladder Atomic weight may be decimal but mass number of atom always a whole number. Rack your Brain How do you find the atomic number?
13. Atomic Structure ISOTOPES, ISOBARS, ISODIPHERS, ISOSTERS AND ISOELECTRONIC (1) Isotopes y Isotopes given by Soddy. y Different atoms of same elements which have similar atomic number but different mass number. y The chemical properties are controlled by the number of electrons. Thus, isotopes of an element show same chemical behaviour but different physical properties. Ex: 1H1, 1H2, 1H3 17Cl35, 17Cl37 6C12, 6C13, 6C14 8O16, 8O17, 8O18 1H1 1H2 1H3 e– 1 1 1 p+ 1 1 1 n 0 1 2 *Similar e– , P+ different n *n + p = 1,2,3 (nucleons) different no. of nucleons *Nuclear charge same Rack your Brain Isotopes and Isobars both do not have same value of e/m. Why? Concept Ladder There are mainly two types of isotopes. These are radioactive and stable isotopes. Stable isotopes have a stable nuclei and do not undergo decay.
14. Atomic Structure (2) Isobars y Isotopes given by Aston. y These are the different atoms of different elements which have similar mass number but different atomic number. y Isobars do not show the same chemical properties. Ex: 6C14, 7N14 17Cl37, 18Ar37 3 2Ce76, 34Se74 2 6Fe58, 27Ni58 6C14 7N14 e– 6 7 p+ 6 7 n 8 7 *Different no of e– , P+ , n *n + p = 14, 14 Same nucleons *Nuclear charge different (3) Neutron Rack your Brain Why isobars have same physical properties? Previous Year’s Question The nucleus of tritium contains [AIPMT] (1) 1 proton + 1 neutron (2) 1 proton + 3 neutron (3) 1 proton + 0 neutron (4) 1 proton + 2 neutron
15. Atomic Structure (3) Isotones The atoms of different element which have the same number of neutrons. Ex: 39 19K 40 20Ca n = 39 – 19 n = 40 – 20 n = 20 n = 20 (4) Isodiaphers The atoms of different element which have the same difference of the number of Neutrons and protons. 5B11 6C12 7N15 8O17 p+ 5 6 7 8 n 6 7 8 9 e– 5 6 7 8 (n – p+) 1 1 1 1 Previous Year’s Question An isotone of 32Ge76 is [AIPMT] (1) 32Ge77 (2) 33As77 (3) 34Se77 (4) 36Sc77 Previous Year’s Question The number of protons, neutrons and electrons in 175 71 Lu , respectively are : [NEET-2020] (1) 71, 104 and 71 (2) 104, 71 and 71 (3) 71, 71 and 107 (4) 175, 104 and 71 Rack your Brain What is the difference between isotopes and isobiaphers?
16. Atomic Structure (5) Isosters The molecules which have the s a m e number of atoms and electrons. CO2 N2O Total Atoms 3 3 No. of e– 6 + 8 × 2 = 22 e– 7 × 2 + 8 = 22 e– (6) Isoelectronic Atoms / ions/ molecules having similar no. of e– Ex: H2O and NH3 10e– 10e– Cl– and Ar 18e– 18e– B3N3H6 and C6 H6 42e– 42e– Previous Year’s Question Be2+ is isoelectronic with [AIPMT-2014] (1) Mg2+ (2) Na+ (3) Li+ (4) H+
17. Atomic Structure (7) Relative Abundance Isotopes of an element occur in different percentages in nature, which is termed as relative abundance. Using this relative abundance the average atomic mass of the element can be calcualted. Ex: 35Cl and 37Cl (75% and 25% abundancve respectively) WAVE y A wave motion is a mean of transfer of energy from one point to another point without any conveying of matter between the points. y When we throw the piece of stone particles on water surface in a pond, we observe circles of ever increasing radius, till these strike on the wall of the pond. y When we put piece of cork on the surface of this water, we observe that the cork moves up and down as the wave passes, but the piece does not travel along with the waves. A wave is characterized by six characterstics (1) Wavelength (l) y It is defined as distance between two nearest crest or nearest through. It is measured in term of a Å (Angstrom), pm (Picometer), nm (nanometer), cm (centimeter), m (meter) 1 10 1 10 1 10 1 10 10 12 9 2 Å m Pm m nm m m , , cm (2) Frequency (n) y Frequency of a wave is a number of waves which pass through a point in 1 sec. it is measured in term of Hertz (Hz), sec–1, or cycle per second (cps) 1 Heartz = 1 sec–1 = 1 cps. Concept Ladder The upper most point of the wave is called crest and the lower most point is called trough. Rack your Brain What frequency is harmful to humans? Previous Year’s Question The frequency of an electromagnetic radiation is 2 × 106 Hz. What is the wavelength in metres [AIPMT] (1) 6.0 × 1014 (2) 1.5 × 104 (3) 1.5 × 102 (4) 0.66 × 10–2
18. Atomic Structure (3) Time period (T) y Time taken for one complete oscillation of wave is known as period (T). Time taken by wave to travel a distance equal to one wavelength. If C is the speed of wave, then C T (4) Wave Number ( n ) y Number of wavelength per unit length. 1 (5) Amplitude (A) y It is the height of depth or crest of a through of a wave. (6) Velocity (C) y It is defined as distance covered by a wave in 1 sec. C Electromagnetic Waves (EMW) y It contains electric and magnetic field. y Energy is always transferred in the form of waves with the speed of light (3 × 108 m/s). y It’s a pure energy waves. y It does not contain mass no medium is required for transmission. y Direction of propagation is perpendicular from both electric field and magnetic field. y There are various types of electromagnetic waves (radiation) which differs from one another in wavelengths. Ex: Cosmic Rays, g-rays , X-rays, U.V, visible, I.R, Micro, Radio. Rack your Brain What is the speed of EMW through the vacuum? Concept Ladder The amplitude of a wave is related to the amount of energy it carries. The sound is perceived as louder if the amplitude increases, and softer if the amplitude decreases. Concept Ladder Near infrared waves are used in remote controls. Far infrared waves are radiant heat. Gamma rays have the greatest energy. Rack your Brain What would happen if there was no electromagnetic spectrum?
19. Atomic Structure Electromagnetic Spectrum y Arrangement of varous types of electrognetic radiations in order of their increasing (or decreasing) wavelengths or frequencies is known as electromagnetic spectrum. Maxwell Theory of Electromagnetic Wave y All the radiations have wave nature which explains interference (linear superposition) and diffraction. y They consist of oscillating electric and magnetic field perpendicular to each other and to the direction of propagation. y All the radiations (radio waves, micro waves, infra red waves, visible, UV, X-rays, g-rays) travel at the speed of light in vaccum. y Energy of electromagnetic wave is proportional to amplitude and not linked with frequence of waves. Rack your Brain How important are EM waves in our lifes? Previous Year’s Question Electromagnetic radiation with maximum wavelength is [AIPMT] (1) Ultraviolet (2) Radiowave (3) X-ray (4) Infrared
20. Atomic Structure Limitations of Maxwell Theory of Electromagnetic Wave y Phenomenon of black body radiations. y Photoelectric effect. y Line spectra of atoms SPECTRUM y When light coming from a source is scatterd by a prism, light of different wavelength are deviated through different angles and get separated. This phenomenon is known as dispersion and such a dispersed light may be received on photographic plate or it’s may be viewed directly by eye. A collection of dispersed light giving its wavelength composition is called a spectrum. Rack your Brain Why was Maxwell theory not accepted? Concept Ladder Most of the light in the universe is invisible to our eyes. The light we can see, made up of the individual colors of the rainbow.
21. Atomic Structure Types of Spectrum (1) Emission spectrum Any substance on heating gets excited on absorbing energy or at a very high temperature or afterwhich radiations are emitted from the substance. The radiations when analysed with the help of spectroscope, spectral lines are obtained. Emission spectrum may be classified as : Concept Ladder Emission spectroscopy is referred to as optical emission spectroscopy because of the light nature of what is being emitted.
22. Atomic Structure (i) Continuous spectrum When sunlight is passed through a prism, it gets dispersed into continuous bands of dif- ferent colours. (ii) Line spectrum If the radiations obtained by the excitation of a substance are analysed with the help of a spectroscope, a series of thin bright lines of specific colours are obtained. There is dark space in between two consecutive lines. This type of spectrum is called line spectrum or atomic spectrum. (2) Absorption spectrum When white light of an incandescent sub- stance is passed through any other sub- stance, this substance absorbs the radiations of particular wavelength from the white light. On analysing the transmiited light we obtain a spectrum in which dark lines of specific wave lengths are observed. These lines constitute the absorption spectrum. Rack your Brain Why is the sun a continuous spectrum?
23. Atomic Structure PLANCK'S QUANTUM THEORY Diffraction and interference are explained by wave nature of electromagnetic radiation. However, some of the observations are given which could not be explained with the help of even the electromagnetic theory 19th century physics (konwn as classical physics) : y Nature of emission of radiation from hot bodies (black -body radiation). y Ejection of electrons from metal surface when radiation strikes it (photoelectric effect) y Variation of heat capacities of solids is a function of temperature. y Line spectra of atoms with special reference to hydrogen. y According to this theory, atoms or molecules can emit or absorb energy only in discrete quantities (small packets) and not in any arbitrary amount. Planck gave name quantum to the smallest quantity of energy that can be emitted in the form of E.N. radiation. Quanta Quantum Definition The radiant energy emitted or absorbed by a body discontinuously in the form of small discrete packets. These packets are called quantum. Concept Ladder Body can emit or absorb energy as hnn, 2hn,n, ...... but it can not emit or absorb energy in fractional values of hnn such as 1.5 hnn, 2.5 hnn. Previous Year’s Question Calculate the energy in joule corresponding to light of wavelength 45 nm. [NEET-2014] (1) 6.67 × 1015 (2) 6.67 × 1011 (3) 4.42 × 10–15 (4) 4.42 × 10–18
24. Atomic Structure y Energy of photon is proportional to frequency and is given by E E = hnn; h = Planck's constant = 6.626 × 10–34 J sec E = λ hc ; υ = λ c y A body can emit or absorb energy only in terms of the integral multiples of quantum, i.e. E = n. hnn, where n = 1, 2, 3, ......... Black Body Radiation y Black body radiation phenomenon first given by Max Planck in 1900. y The ideal body, which emits and absorbs radiations of all frequencies, is called black body and the radiation emitted by that body is known as black body radiation. Previous Year’s Question The value of Planck's constant is 6.63 × 10–34 Js. The speed of light is 3 × 1017 nm s–1. Which of the given values is closest to the wavelength in nanometer of a quantum of light with frequency of 6 × 1015 s–1? [NEET-2013] (1) 50 (2) 75 (3) 10 (4) 25 Concept Ladder Blackbody is a surface that absorbs all radiant energy falling on it. The term arises because incident visible light will be absorbed rather than reflected, and therefore the surface will appear black.
25. Atomic Structure 3 × 108 photons of a certain light radiation are found to produce 1.5 J of energy. Calculate the wave length of light radiation ? ETotal = n × {hu} ETotal = n × λ hc 1.5 J = × × × × λ –34 8 8 6.6 10 3 10 3 10 l = 3.96 × 10–17 m Q1 A1 100 watt bulb emits monochromatic light of wave length = 400 nm. Calculate the no. of photons emitted per second? (1) 5 × 1020 (2) 3 × 1020 (3) 4 × 1020 (4) 2 × 1020 (4) t = 1 s Etotal = λ nhc 100 = × × × × × –34 8 –9 n 6.6 10 3 10 400 10 n = 2 × 1020 no. of photons per second Q2 A2
26. Atomic Structure PHOTOELECTRIC EFFECT The ejection of electrons when light of certain minimum frequency called as threshold frequency is incident on a metal surface is called as photoelectric effect. Threshold Frequency The minimum frequency of incident light which can cause photo electric emission i.e. this frequency is just able to eject electrons with out giving them additional energy. Work Function The minimum quantity of energy which is re- quired to remove an electron to infinity from the surface of a given solid, usually a metal. Incident energy = Work Function (φ) + K.E.max Ei = φ + (K.E.)max hu = υ + υ2 0 e 1 h m 2 Where me is mass of the electron and v is the velocity associated with the ejected electron. Some facts of Photoelectric Effect y There is zero time lag between incidence of light and emission of photoelectrons. Concept Ladder The maximum kinetic energy of photoelectrons depends on the frequency of incident radiation; but, it is independent of the intensity of light used. Rack your Brain Which metal is best for photoelectric effect? Previous Year’s Question In photoelectric effect, the kinetic energy of photoelectrons increases linearly with the [AIPMT] (1) Wavelength of incident light (2) Frequency of incident light (3) Velocity of incident light (4) Atomic mass of an element
27. Atomic Structure y For the emission of photoelectrons, frequency of incident light must be equal to or greater than the threshold frequency. y Rate of emission of photoelectrons from a surface of metal is directly proportional to the intensity of incident light. Concept Ladder The minimum potential at which the photoelectric current becomes zero is called stopping potential. The threshold frequency n0 for a metal is 6 × 1014 s–1. Calculate the kinetic energy of an electron emitted when radiation of frequency n = 1.1 × 1015 s–1 hits the metal. K.E. = 1 2 meV2 = h (n – n0 ) ∴ K.E. = (6.626 × 10–34) (1.1 × 1015 – 6 × 1014) ∴ K.E. = (6.626 × 10–34) (5 × 1014) = 3.313 × 10–19J Q3 A3 BOHR'S ATOMIC MODEL It is a quantum mechanicla model. This mod- el based onquantum theory of radiation and clas- sical law of physics. This model explain the sta- bility of the atom and emission of sharp spectral lines. Rack your Brain Do emitted photoelectrons have same kinetic energy?
28. Atomic Structure Bohr Model's Postulates y Atom has a central core nucleus where the protons and neutrons are present. Size of the nucleus is very small. y Negatively charged electron are revolving around the nucleus in the same wasy as the planets are revolving around the sun. The path of electron is circular. y Electrons can revolve only in those orbits whose angular momentum (mvr) is integral multiple of h 2p . i.e. mvr nh 2 y Absorption or emission of radiation by an atom takes place when an electron jumps from on stationary orbit to another. y The radiation is emitted or absorbed as a single quantum (photon) whose energy is equal to the difference in energy of the electron in the two orbitals involved. Thus, De = hn, where h = Planck's constant and n = frequency of the radiant energy. Hence the spectrum of the atom will have certain fixed frequence. y The lowest energy state (n = 1) is called the group state. After absorption of energy,electron gets excited and jumps to an outer orbit. It has to fall back to a lower orbit with the release of energy. Rack your Brain Angular momentam is integral multiple of h/2p. Why not fractional multiple is possible? Concept Ladder Bohr's theory satisfactorily explains the spectra of species having opne electron, viz. H, He+, Li2+ etc. Concept Ladder mvr nh 2 r n Z A 0 529 2 . v Z n m 2 188 106 . / sec E Z n eV atom 13 6 2 2 . /
29. Atomic Structure Radius of the Bohr's Orbit Let us consider an electron of mass 'm' and charge 'e' is revolving around nucleus having charge 'Ze' (where Z is atomic number & e is charge) with a linear or tangential velocity of 'v'. Further, let us consider that 'r' is radius of orbit in which electron is revolving. According to Coulomb's law,electrostatic force of attraction (F) between moving electron and nucleus is – F KZe r = 2 2 Where : K = constant 1 4 9 109 2 2 o Nm C/ and the cnetripetal force F mv r = 2 Hence mv r KZe mr 2 2 = or v KZe mr 2 2 1= ......( ) From the postulate of Bohr, mvr nh 2 or v n h m r 2 2 2 2 2 2 4 2 ......( ) mvr= π 1h 2 π 2h 2 π 3h 2 π 4 h 2 π 5h 2 Previous Year’s Question If r is the radius of the first orbit, the radius of nth orbit of H-atom is given by [AIPMT] (1) rn2 (2) rn (3) r/n (4) r2n2
30. Atomic Structure From equation (1) and (2) r n h mKZe 2 2 2 2 4 On putting value or e, h, m, r n Z A 0 529 2 . Velocity of an electron in Bohr's Orbit The total energy of an electron is revolving in a particular orbit is — mvr nh v nh mr 2 2 Purring the value of r in above equation then v nh mZe mn h v Ze nh 4 2 2 2 2 2 2 2 on purring the values of e and h v Z n m 2 188 106 . / sec Calculation of energy of an electron The total energy of an electron revolving in a particular orbit is — T.E. = K.E. + P.E. The K.E. of an electron = 1 2 2 mv and the P.E. of an electron KZe r 2 Hence, T E mv KZe r . . ......( ) 1 2 32 2 But mv r KZe r or mv KZe r 2 2 2 2 2 = = Substituting value of mv2 in the equation (3) T E KZe r KZe r KZe r . . 2 2 2 2 So, T E KZe r . . 2 2 Previous Year’s Question The energy of second Bohr orit of the hydrogen atom is –328 kJ mol– 1; hence the energy of fourth Bohr orbit would be [AIPMT] (1) – 41 kJ mol–1 (2) – 82 kJ mol–1 (3) – 164 kJ mol–1 (4) – 1312 kJ mol–1 Rack your Brain What will be the value of Kinetic energy and Potential Energy at n = ∞? Concept Ladder Bohr's atomic model explained the stability of an atom. According to Bohr, an electron revolving in a particular orbit cannot lose energy. Therefore, emission of radiation is not possible as long as the electron remains in one of its energy levels and hence there is no cause of insatbility in his model.
31. Atomic Structure Substituting value of 'r' in the equation of T.E. E kZe Ze mk n h Z e mk n h 2 2 2 2 2 2 2 4 2 2 2 2 4 2 Thus, the total energy of an electorn in nth orbit is given by E Z e mk n H Z n eV atom Z n J atom 2 13 6 21 8 10 2 2 4 2 2 2 2 2 19 2 2 . / . / 313 6 2 2 . / Z n Kcal mole Relationship between P.E., K.E. & T.E. P E KZe r KZe r T E KZe r T E P E K E . . , K .E . , . . . . . . . . 2 2 2 1 2 1 2 2 Previous Year’s Question Based on equation E = – 2.178 × 10–18 J(Z2/n2), certain conclusions are written. Which of them is not correct? [NEET-2013] (1)) Equation can be used to calculate change in energy when electron changes orbit. (2) For n = 1, electron has a more negative energy than it does for n = 6 which means that electron is more loosely bound (3) Negative sign in equation simply means that energy of electron bound tot he nucleus is lower than it would be if electrons were at the infinite distance from nucleus. (4) Larger the value of n, larger would be the orbit radius..
32. Atomic Structure Calculation of the number of revolutions of the electron in an orbit per second Number of revolutions per sec. velocity of the electron Cir ccumference of the orbit On substituting v r nh mr r2 2 1 2 [ tthe value of v from mvr nh nh mr 2 4 2 2 ] No. of revolutions per second nh mr nh m mze k n h4 4 4 2 2 2 2 2 2 2 2 2 2 4 3 3 3 4 mz e k n h Ionization Energy / Ionization potential Minimum energy required by an electron to leave the ground state: For Ex: H (IP)H = – (13.6) = 13.6 Separation Energy Minimum amount of energy required to escape an e– from an excited state 2 → ∞ 3 → ∞ Previous Year’s Question In hydrogen atom, energy of first excited state is –3.4eV. Then find out K.E. of same orbit of hydrogne atom. [AIPMT] (1) +3.4 eV (2) +6.8 eV (3) –13.6 eV (4) +13.6 eV
33. Atomic Structure Failure of Bohr Model y The theory was very successful in predicting and accounting the energies of line spectra of hydrogen i.e. one electron system. It could not explain theline spectra of atoms containing more than one electron. y Theory does not explain the presence of multiple spectral lines. y Theory does not explain splitting of spectral lines in magnetic field (Zeeman effect) and in electric field (Stark effect). Intensity of spectral lines was also not explained by the Bohr atomic model. y This theory could not explain uncertainty principle. The Bohr-Sommerfeld Theory For explaining fine structures of spectral lines Sommerfeld introduced two modification in Boht's theory. y According to Sommerfeld, path of an electron around nucleus, is an ellipse with nucleus at one of the foci. Circular orbit is special case of the ellipse. y Velocity of electron moving in an elliptical orbit varies at different parts of the orbit. This causes relavitistic variation in mass of moving electron. Therefore, he took into account relativistic variation of mass of electron with velocity. Therefore, this is known as relativistic atom model. Limitations of the Bohr-Sommerfeld Theory y Sommerfeld's theory was able to give an explanaiton of the fine structure of the spectral line of hydrogen atom. But he could not predict the correct of spectral lines. Previous Year’s Question Who modified Bohr's theory by introducing elliptical orbits for electron path? [AIPMT] (1) Rutherford (2) Thomson (3) Hund (4) Sommerfeld Concept Ladder Bohr-Sommerfeld theory described the atom in terms of two quantum numbers, while Bohr ahd originally used only one quantum number. Rack your Brain What is the success of the Sommerfeld model?
34. Atomic Structure Which one is in correct about the angular momentum? (1) = π h mvr 2 (2) = π h mvr (3) = π 3h mvr 2 (4) = π 3h mvr 4 (4) (1) n = 1 (2) n = 2 π 2h 2 (3) mvr = π 3h 2 n = 3 (4) mvr = π 3h 4 n = 3/2 Q4 A4 For H-atom, calculate radius Z = 1 ( ) = 2 n H n r 0.529 Å Z ( ) = 2 1 H r 0.529 1 Å ( ) = 2 2 H r 0.529 2 Å ( ) = 2 3 H r 0.529 3 Å ( ) = 2 n H r 0.529 n Å { }= 2 n 1r n r (r3)H = (9r1)H rn = 16r1 r5 = 25r1 Q5 A5 () PE = – x = 3.02 KE = +x 2 = + = + 3.02 .51 2 The P.E. of an e– in the H– atom is –3.02 eV. Then find out (1) K.E. (2) T.E. (3) Orbit (4) Radius Q6 A6
35. Atomic Structure T.E = = = x –3.02 – –1.51 2 2 = = 2 2 –13.6Z –1.51 n =2 –13.6 –1.51 n n2 = 9 ; n = 3 [r3 = 0.529 × 9 Å 1 ] If I.P of H atom is ‘x’ eV. Then calculate the required energy to exited e– from 2nd to 3rd orbit : (1) 2 x 36 (2) 1 x 8 (3) 5 x 36 (4) 7x 3.6 Q7 (3) I.P = – E1 = x E1 = –x = –13.6 x = 13.6 = = − = 3 2 2 2 –13.6 –13.6 1 1 5 E – E – 13.6 x 3 2 4 9 36 A7 HYDROGEN SPECTRUM y Hydrogen spectrum is an example of atomic or line emission spectrum. y Whenever an electric discharge is passed to hydrogen gas at low pressure, a bluem light is emitted. The light shows discontinuous line spectrum of several isolated sharp lines through prism. y All these lines of H-spectrum have Lyman, Balmer, Paschen, Brackett, Pfund and Humphrey series. y Wavelength of various H-lines Rydberg introduced the following expression, 1 1 1 1 2 2 2 c R n n R is a Rydberg's constant its value is 109,67800 m–1. Concept Ladder The spectral series are important in astronomy for detecting the presence of hydrogen and calculating red shifts.
36. Atomic Structure Concept Ladder Maximum number of lines produced when an electron jumps from nth level to group level n n 1 2 Rack your Brain Why the line spectra of two elements are not identical? Total Number of spectral Lines = ( ) ( )+2 1 2 1n – n n – n 1 2 Ex In the H- atom if an e– moves from 6th to 3rd orbit by transition is multi steps. Then find (i) Total no of spectra lines (ii) No of lines in visible region (iii) No of lines in UV region (iv) No of lines is Brackett series (v) No of lines in Infrared series (vi) No of lines in Paschen series Sol Lyman → O, Balmer → O (UV) (IR) Paschen → 3 Brackett → 2 (IR) P– Fund → 1 (IR)
37. Atomic Structure SERIES 7 6 5 4 3 2 Lyman 6 5 4 3 2 I (UV) Balmer 5 4 3 2 1 0 visible Paschen 4 3 2 1 0 Infared Ray (1) Brackett 3 2 1 0 P-fund 2 1 0 Humphry 1 0 (21) (15) (10) (6) (3) A certain electron transition from an excited state of H-atom in one or more steps give rise of 5 lines in U.V region. Then how many lines does this transition produce in IR region? (1) 6 (2) 7 (3) 8 (4) 9 (1) 5 → U.V 4 → visible 3 → IR 2 → IR 1 → IR IR = → 4 UV 3 visible 2 IR 1 IR Q8 A8 The e– in a hydrogen atom transition from the Bohr orbit 5 to the orbit 2. Calculate the wavelength of photon emitted during transition. Given h = 6.6×10–34 J/sec. C= 3× 108 m/s. RH = 2.18 × 10–19 J = HR R hc = λ 2 2 2 1 2 1 1 1 RZ – n n Q9 A9
38. Atomic Structure
39. Atomic Structure Ex Emission Line Any particular series spectrum Lyman series ∆ = υ = λ hc E h Lyman last line (∞→1) DE → max u → max * = λ 2 2 2 1 2 1 1 1 Rz – n n n2 → n1 ( l) R = 109678 cm–1 = 1097.0 cm–1 = 1 912Å R Calculate the l of 1st lined and last line of Balmer series in H-spectrum ? = λ 2 2 2 1 1 1 RZ – 2 3 = = 1 1 R – 4 9 = λ 1 5R 36 λ = × = × 36 1 36 912Å 5 R 5 Last line ∞ → L = λ ∞ 2 2 1 1 1 R – 2 = λ 1 1 R 4 λ = 4 R = 4 × 912 Å Q10 A10 Previous Year’s Question Which of the following series of transitions in the spectrum of hydrogen atoms falls in visible region: [NEET-2019] (1) Brackett series (2) Lyman series (3) Balmer series (4) Paschen series
40. Atomic Structure WAVE MECHANICAL MODEL OF AN ATOM The model consists of following : (A) de-Broglie concept (Dual nature of Matter) (B) Heisenberg’s Uncertainty principle. DUAL NATURE OF MATTER (WAVE NATURE OF ELECTRON) l ∝ 1 p or l = h p (Here h = Planck’s constant, p = momentum of electron) Momentum (p) = Mass (m)×Velocity (v) ∴ l = h mv We know that according to Bohr theory, mvr = π nh 2 or 2pr = nh mv ∴ 2pr = nl mvr = π nh 2 Previous Year’s Question In hydrogen atom, the de Broglie wavelength of an electron in the second Bohr orbit is [Given that Bohr radius, a0 = 52.9 pm] [NEET-2019] (1) 211.6 pm (2) 211.6 p pm (3) 52.9 p pm (4) 105.8 p pm Concept Ladder Circumference of orbit is equal to integral multiple of wavelength (l), i.e., 2pr = nl.
41. Atomic Structure Heisenberg uncertainty principle When an electron is considered to be a wave as suggested by de-Broglie, it is not possible to identify the exact position and velocity of the electron more precisely at a given instant since the wave extends throughout a region of space. Dx.Dp ≥ π h 4 or Dx. mDv ≥ π h 4 or Dx.Dv ≥ π h 4 m or Dt×Dx× ∆ ≥ ∆ π p h t 4 Where h is Planck’s constant. F × Dt × Dx ≥ π h 4 DE×Dt ≥ π h 4 From above description it is clear that according to de-Broglie there is similarity between wave theory and Bohr theory. A ball weight 25 g moves with a velocity of 6.6×104 cm/s then find out the de- Broglie l associated with it. l = h mv = − × × × × 34 7 4 6.6 10 10 erg 25 6.6 10 cm / s s = 0.04×10–31 cm = 4 × 10–33 cm Q11 A11 If the uncertainity in position of a moving particle is 0 then find out Dp.Q12 Previous Year’s Question Which one is the wrong statement? [NEET-2017] (1) The unceratnity principle is E t h 4 (2) Half filled and fully filled orbitals have greater stability due to greater exchange energy, greater symmetry and more balanced arrangement. (3) Then energy of 2s-orvbital is less than the energy of 2p-orbital in case of hydrogen like atoms. (4) de-Broglie's wavelength is given by h mv where m = mass of particle, v = group velocity of the a particle Rack your Brain Why possiblity of the electron in the nucleus is zero?
42. Atomic Structure WAVE MECHANICAL MODEL OF ATOM y This model was developed by Erwin Schrodinger in 1926. y This atomic model is based on particle and wave nature of electron is known as wave mechanical model of the atom. y This model describes the electron as a three- dimensional wave in the electronic field of positively charged nucleus. y Schrodinger derived an equation which described wave motion of an electron. The differential equation is : d dx d dy d dz m h E V 2 2 2 2 2 2 2 2 8 0 where x, y and z are cartesian co-ordinates of the electron m = mass of the elecron E = total energy of electron V = potential energy of electro n h = planck's constna Y = wave function of the electron 2 2 2 8 0 m K E h . . Significance of Y Wave function is regarded as the amplitude function expressed in terms of coordination x, y and z. Wave function can have negative or D x Dp ≥ π h 4 or Dp ≥ π∆ h 4 x or Dp ≥ π × h 4 0 or Dp ≥ ∞ A12 Previous Year’s Question The uncertainty in momentum of an electron is 1 × 10–5 kg m/s. The uncertainty in its position will be [AIPMT] (1) 5.27 × 10–30 m (2) 1.05 × 10–26 m (3) 1.05 × 10–28 m (4) 5.25 × 10–28 m Concept Ladder Berhaviour of electrons and other microscopic particles, a new branch of science called quantum mechanics was developed.
43. Atomic Structure positive values depending upon the values of coordinates. Significance of Y2 Y2 is a probability factor. It describes the probability of fi8nding an electron within a small space. The spacein which there is maximum probability of finding an electron is termed as orbital. Variations of Radial Wave Function (R) (i) Plots of radial wave function R against the distance r The variation of the radial part of the orbital wave funcitons for 1s, 2s and 2p orbitals. The radial funcitn value changes form positive to zero then to negative. The region where this function reduces to zero is called nodal surfaces or simply nodes. (ii) Radial probability density (R2) Square of radial wave function, R2, is the measure of the probability of finding the electron in a unit volume around a particular point and is called probability density. Previous Year’s Question The graph between |Y|2 and r (radial distance) is shown below. This represents [AIPMT] (1) 3s orbital (2) 1s orbital (3) 2p orbital (4) 2s orbital Rack your Brain What is the significance of the wave function Y?
44. Atomic Structure s- Subshell (iii) Radial distribution function, (4pr2R2) Probability density of finding electron at a point at a distance r form the nucleus. Since the atoms have spherical symmetry, it is more useful to discuss the probability of finding the electron in a sphericla shell between the spheres of radii r + dr and r. Node Nodal point (φ=0) Nodal plane Nodal plane / Angular Node = l Nodal surface Nodal surface / Radial Nodes = n – l – 1 Radial Nodes Radial Nodes →→→→→→→ Angular Nodes Rack your Brain How do you find number of nodal planes in a molecular orbital? Previous Year’s Question Orbital having 3 angualr nodes and 3 total nodes is [NEET-2019] (1) 5p (2) 3d (3) 4f (4) 6d Definition The plane / surface in which probability of finding electron is zero is called as Node.
45. Atomic Structure Radial Nodes (n –l –1) Concept Ladder The number of nodes is always one less than the principal quantum number : Nodes = n - 1. In the first electron shell, n = 1. the 1s orbital ha no nodes. The 3s, 3p and 3d orbitals have two nodes, etc. Definition To obtain the information about an electron Identification numbers are required. These numbers are called Quantum numbers. Angular Node l = 0 RN = n – l – 1 = n = 2 n – 2 [RN] 1s 0 2px 0 2s 1 3px 1 3s 2 4px 2 QUANTUM NUMBERS y Quantum numbers are to specify and display to complete information about size, shape and orientation of the orbital.
46. Atomic Structure Types of Quantum Numbers (1) Principal Quantum Number (n) (2) Azimuthal Quantum Number (l) (3) Magnetic Quantum Number (m) (4) Spin Quantum Number (s) (1) Principal Quantum Number (n) y It is the most important quantum number as it determines the size and to large extent the energy of the orbital. y The average energy of the electron is directly proportional to the principal quantum number. y The size of an orbital will increase an increase in the principal quantum number. y Maximum number of electrons in a shell is given by 2n2. Exclusive identity of an e– *n → name, size energy of shell n = 1 K Shell n = 2 L n = 3 M n = 4 N n = 5 O n = 6 P Angular momentum (J/L) mvr= π nh 2 J3 > J2 > J1 Max. No of e– in a shell = 2n2 K n = 1 (2) L n = 2 (8) M n = 3 (18) N n = 4 (32) Previous Year’s Question The orientation of an atomic orbital is governed by [NEET] (1) principal quantum number (2) azimuthal quantum number (3) spin quantum number (4) magnetic quantum number Concept Ladder Quantum number are important because they can be determine the elctron configuration, probale location of electrons, ionization energy, atomic radius.
47. Atomic Structure Value of l 0 1 2 3 Sub-shell notation s p d f Number (2l + 1) of orbitals 1 3 5 7 (2) Azimuthal Quantum Number (l) y This is also known as orbital angular momentum or subsidiary quantum number. y Azimuthal quantum number (l) gives the information about subshell in which the electron is located. y Orbital Angular Momentum ( ) + π h 1 2 ( )+ 1 s l = 0 → 0 p l = 1 → 2 { } d l = 2 → 6 { } f l = 3 → 12 { } Concept Ladder The name 'azimuthal quantum number' for l was originally introduced by Sommerfeld, who refiend Bohr's semi-classical model by replacing circular orbits with elliptic ones. The spherical orbitals were similar (in the lowest-energy state) to a rope oscillating in a large 'horizontal' circle.
48. Atomic Structure y Max. No. of e– in a subshell = (4l + 2) s l = 0 2 for any given n, l will be from [0 to n =–1] p l = 1 6 d l = 2 10 f l = 3 14 Shape of subshell y s, p, d and f are taken from spectroscopic terms sharp, principal, diffuse, and fundamental, respectively. y In a multi electron atom, the energy associated with an electron depends both on n and l. n l Subshell notation 1 0 1s 2 0 2s 2 1 2p 3 0 3s 3 1 3p 3 2 3d 4 0 4s 4 1 4p 4 2 4d 4 3 4f Concept Ladder The magnetic quantum number describes the energy levels available within a subshell and yields the projection of the orbitgal angular momentum along a specified axis. Previous Year’s Question The following quantum number are possible for how many orbitals? n = 3, l = 2 and m = +2 [NEET] (1) 1 (2) 2 (3) 3 (4) 4 Previous Year’s Question What is the maximum numbers of electrons that can be associated with the following set of quantum numbers? n = 3, l = 1 and m = –1 [NEET-2013] (1) 4 (2) 2 (3) 10 (4) 6
49. Atomic Structure
50. Atomic Structure (3) Magnetic Quantum Number (m) y Magnetic quantum number was proposed by Land. y The magnetic quantum number gives information about the spatial orientation of orbitals. These different orientations are called orbitals. y It is denoted by m and its value depend on l values. y The possible value of m range from -l through 0 to +l. y Total number of orbitals = (2l + 1) y Number of obitals in a shell is n2. (4) Spin Quantum Number (s) y In 1925, George Uhlenbeck and Samuel Goudsmit proposed the presence of the fourth quantum number and depicted it as the elctron spin quantum number. y Two electrons that have different s, values ± 1 2 and both electrons have opposite spins. y An orbital can hold maximum two electrons. y Spin angular momentum is depicted by the symbol ms. The value of ms: s s s h 1 2 Previous Year’s Question The correct set of four quantum number for the valence electron of rubidium atom (Z = 37) is [NEET-2012] (1) 5, 1, 1, +1/2 (2) 6, 0, 0, +1/2 (3) 5, 0, 0, +1/2 (4) 5, 1, 0, +1/2 Concept Ladder Zeeman effect : Splitting of lines of atomic spectrum in magnetic field. Stark effect : Splitting of lines of atomic spectrum in electric field. Previous Year’s Question Which of the following pairs of d-orbitals will have electron denstiy along the axis? [NEET-2012] (1) d dz xz2 , (2) d dxz yz , (3) d dz x y2 2 2, − (4) d dxy x y , 2 2 −
51. Atomic Structure y If all the electrons in an atom or molecule are paired. They behave as dimagnetic substance. It is weakly repelled by the magnetic field. y If atoms or molecules of a substance have one or more unpaired electrons, it behaves as a paramagnetic substance. it is weakly attracted by the magnetic field. y Magnetic moment n n BM2 Where, n = number of unpaired electrons Difference between orbit and orbital Orbit Orbital 1. An orbit refers to the circular path in which an electron revolves around the nucleus. 1. An orbital refers to the region of space having the maximum probability of finding an electron around the nucleus. 2. An orbit represents the motion of an electron arougn the nucleus in a plane. 2. An orbital represents the motion of an electron around nucleus in three- dimensional space. 3. An orbit (n) can accommodate a maximumn of 2n2 electrons. 3. An orbital can accommodate a maximum of two electrons. 4. Orbits are desinated as K, L, M etc. or 1, 2, 3etc., from the nucleus outwards. 4. Orbitals are designated as dxy, dyz, dzx, dx2-y2, dz2, px, py, pz etc. 5. Orbits are circular in shape. 5. Orbitals have different shapes, e.g., s orbitals are spherically symmetrical whereas p orbitals are dumbbell shaped. Concept Ladder The spin of electrons is responsible for most of the magnetic properties of atoms, molecules, or ions. Due to their spin, electrons behave as tiny magnets.
52. Atomic Structure
53. Atomic Structure RULES FOR FILLING OF ORBITALS IN AN ATOM (1) Aufbau Principle The principle states that electrons are added progresively to the various orbitals in the order of increasing energies. The electrons first occupy the lowest energy orbital avaiable to them and enter into higher energy orbitals only after lower energy orbitals are filled. (n +l) Rule (For multi electron species) The subshell with lowest (n + l) value is filled up first, when two or more subshell have same (n + l) value then the subshell with lowest value of n is filled up first. (2) Hund’s Maximum Multiplicity Rule According to the Hund’s rule orbital available in the subshell are first filled singly with parallel spin electron before they begin to pair this means that pairing of electrons occurs with the introduction of second electron. Concept Ladder Afbau principle proposed by Niels Bohr in the early 1920s, the principle was a tool for obtaining a picture of the atomic constitution, i.e., the arrangement of electrons on orbits around the nucleus. Previous Year’s Question In a given atom no two electrons can have the same valus for all the four quantum numbers. This is called [AIPMT] (1) Hund's Rule (2) Aufbau Principle (3) Uncertainty Principle (4) Pauli's Exclusion Principle.
54. Atomic Structure (3) Pauli Exclusion Principle According to this rule no two electron in an atom can have same values of all four quantum numbers. Ex: 6C12 → 1s2 2s2 2p2 Px Pz Py n 1 2 2 l 0 0 1 m 0 0 +1, 0, –1 s +½, –½ +½, –½ +½, +½ ELECTRONIC CONFIGURATION OF ATOMS In an atom, electrons are distributed among various orbitals very much in accordance with rules governing the filling of different orbitals. Ex Notation form of Na — 1s22s22p63s1 Orbital diagram from of Na Condensed form of Na — [Ne] 3s1 STABILITY ORDER OF COMPLETELY FILLED AND HALF FILLED SUB-SHELLS The ground state electronic configuration of atom corresponds to the lowest energy state and gives higher stability. The electronic configuration of most of the atoms follows the basic rules. Certain elements such as Cr or Cu do not follow the rules because the two sub-shells 4s and 3d slightly differ in energy, i.e., 4s is slightly lower in energy than 3d orbital. So the valence electronic configuration are 3d54s1 and 3d104s1 respectivley, and not 3d44s2 and 3d94s2. The extra stability of half-filled and fully filled electronic configuration can be explained in Definition Distribution of electrons into orbitals of an atom is called its electronic configuration. Concept Ladder The Pauli exclusion principle helps explain a wide variety of physical phenomena. Electrons have to stack within an atom, i.e. have different spins while at teh same electron orbital. Previous Year’s Question If n = 6, the correct sequence for filling of electrons will be [AIPMT-2011] (1) ns (n ) f (n ) d np2 1 (2) ns d f (n ) (n ) np1 2 (3) ns (n ) f np (n ) d2 1 (4) ns np (n ) d (n ) f1 2
55. Atomic Structure terms of symmetry and exchange energy. Symmetrical distribution of electrons The electronic configurations in which all the orbitals of the same sub-shell are either completely filled or half filled have relatively more symmetrical distribution of electrons. So their shielding of one another is relatively small and the electrons are more strongly attracted by the nucleus. Ex: Cr Exchage energy Exchange means shifing of electrons from one orbital to another within same sub-shell. Energy gets released when electrons exchange their positions and the energy is called exchange energy. For maximum number of exchanges, the maximum the energy released and the maximum the stabilisation. Half-filled and fully-filled degenerate orbitals have more number of elctron exchanges, and consequently, they have larger exchange energy of stabilisation. Ex Cr (For 3d44s2) Previous Year’s Question The outer electronic configuratino of Gd (Z = 64) is [NEET-2013] (1) 4f55d46s1 (2) 4f75d16s2 (3) 4f35d56s2 (4) 4f45d56s1 Concept Ladder Stability of electronic configuration depends on : (1) Half-filled and Full-filled (2) Symmetrical distribution (3) Exchange Energy Previous Year’s Question The electronic configuratino of Cu (Z = 29) is [AIPMT] (1) 1s22s22p63s23p64s23d9 (2) 1s22s22p63s23p63d104s1 (3) 1s22s22p63s23p64s24p65s25p1 (4) 1s22s22p63s23p64s24p63d3
56. Atomic Structure Cr (For 3d54s1)
57. Atomic Structure If the mass of e– is assumed to be doubled the mass of proton is doubled and mass of neutron is halved, Then calculate the atomic wt. of 8016 and % by which it is increased? (1) 20 amu, 25% (2) 30 amu, 25 % (3) 40 amu, 25% (4) 45 amu, 25 % (1) 1e– = negligible, 1P+ = 1 amu, 1n ≈ 1 amu 16 8O = ⇒– e 8 0 amu, + = ⇒p 8 8 amu, = ⇒n 8 8 amu Total 16 amu Double e– = X, p+ = 16 amu, n = 4 amu Total 20 amu % increment: × = 4 100 25% 16 Q13 A13 If the mass of proton is halved, mass of neutron is tripled and mass of e– remains unchanged. Then calculate the atomic weight of 6C12 and the % increment: (1) 22 amu, 75% (2) 21 amu, 75% (3) 20 amu, 50% (4) 15 amu, 60% (2) 12 6C e– = → X p+ = → 6 → 3 amu n = → 6 → 18 amu Total 12 21 amu (% increment = × 9 100 12 = 75%) Q14 A14 If an element has two isotopes forms 18 and 20 and the % abundance in nature are 20% and 80% respectively. Then calculate the avg. atomic wt. of element ? (1) 21.6 (2) 19.6 (3) 20.6 (4) 22.6 Q15
58. Atomic Structure (2) 18 A X 20 A X Average atomic weight = × + × = 20 80 18 20 19.6 100 100 A15 The wave number of a beam of light is 400 cm–1 calculate the wavelength in terms of nanometer. Also find its frequency. υ = υ = = λ λ = = × 1 –1 –7 400 cm 1 400 cm 1 1 cm 400 400 10 nm × υ = = λ × 8 –2 c 3 10 1 10 m 400 Q16 A16 A radio station is broadcasting program at 108 frequency if the distance b/w radio station and the receiver is 3 lakh meter then, how long would it take the signal to reach the receiver. Find out the value of l and υ ? (1) 3m, 0.22 m–1 (2) 3m, 0.33 m–1 (3) 4m, 0.33 m–1 (4) 1m, 0.30 m–1 (2) { } = × υ = λ 8 3 300000 m 1 t S 3 10 m / s 10 c 10+8 = × ⇒ λ = λ 8 3 10 3 υ = = λ –11 1 m 3 Q17 A17 Radius of 1st Bohr orbit of H–atom is 0.52 × 10–8 . Calculate the radius of 1st orbit of He ? (1) 0.16 × 10–8 cm (2) 0.36 × 10–8 cm (3) 0.46 × 10–8 cm (4) 0.26 × 10–8 cm Q18
59. Atomic Structure (4) ∝ 2 n n r Z ( ) ( ) + = = 2 1 H 1 1 2 1 2 2He r n / z2 1 r n / z ( ) + = 1 H He r r 2 = = 2 2 1 / 1 2 1 / 2 = × = × –8 –80.52 10 0.21 10 2 cm Orbit Z H 1 1 He+ 1 2 ∝ 1 r Z A18 I.P of H– atom is 13.6 eV. Calculate the I.P of He+ & Li+2 H I.P = –E1 E1 = –13.6 He+ I.P = –E1 E1 = –13.6 × 4 Li+2 I.P = –E1 = + (9 ×13.6) = –13.6× 9 I.P = {13.6} × Z2 Q19 A19 A photon of energy 12.09 eV is completely absorbed by a H–atom initially in ground state find out the orbit in which electron is revolving (1) 2 (2) 3 (3) 4 (4) 5 (2) –13.6 + 12.09 = –1.51 = –13.6 ( ) 2 1 nn2 = 9 n = 3 Q20 A20 An e– of an atom having z = 5 revolves around a nucleus the energy required to excite the e– from 3rd to 4th orbit will be : (1) 12.5 (2) 13.5 (3) 14.5 (4) 16.5 Q21
60. Atomic Structure (4) × × = 4 3 2 2 –13.6 25 –13.6 25 E – E – eV 4 3 = 13.6 × 25 1 1 – 9 16 = 13.6 × 25 × × 7 eV 16 9 = 16.5 Trick → ( ) × Z2 ( ) Z = 5 3 → 4 10.2 1.89 0.660.31 0.66 × 25 = 16.5 A21 Compare the velocities of e– in the first excited state of He+ and 2nd excited state of Li+2 (1) 2 : 1 (2) 1 : 2 (3) 1 : 1 (4) 2 : 3 (3) → He+ Li+2 Z 2 3 n 2 3 [ ∝ Z V n ] 1 = 1 Q22 A22 The relative abundance of two rubidium isotopes 85 37Rb 87 37Rb 75% 25% (1) 75.5 (2) 86 (3) 86.5 (4) 87.5 (2) Find out average atomic wt. 85 87 75% 25% 86 Q23 A23
61. Atomic Structure Chapter Summary Atom is the fundamental unit of matter which is further indivisible i.e. atom can neither be created nor be destroyed. Atomic theory of matter was first proposed by John Dalton. Discovery of subatomic particles namely electron and proton. Electron is discovered through cathode ray discharge tube experiment. They consist of negatively charged particles which are known as electrons. The characteristics of cathode rays is independent of electrodes and nature of gas present in cathode tube. Measurement of e/m for electron. The value of e/m has been found to be 1.7588 × 1011 C/Kg. Charge on an electron is 1.602 × 10–19 C. Mass of the e– can be calculated from the value of e/m and the value of e. The characteristics of anode rays or canal rays is dependent on nature of gas present in cathode tube. Charge to mass ratio of particle depends on the gas from which they generated. Atoms are made of three particles electron, protons and neutrons. Rutherford’s Model: Atom of an element consist of a small positive charged nucleus situated at the centre of the atom. Electrons are distributed in different concentric circular paths around the nucleus called orbits. Atomic radius is of the order 10–10 m while nucleus is 10–15 m. Atomic no. of an element = Total no. of protons present in the nucleus. Protons and neutrons present in nucleus collectively called nucleons. Mass no. of an element = No. of protons + No. of neutrons Isotopes: They have same atomic number but different atomic weight and have same chemical properties. Isobar: The different atoms which have same atomic masses but different atomic number are called as Isobar. Isotone: When elements have same number of electrons of neutron are called as Isotones. Isoelectronic: Ion or atom or molecule or species which have the same number of electrons are called as isoelectronic species. Electromagnetic Wave Radiation: The oscillating electrical/magnetic field are electromagnetic radiations. Both electrical and magnetic field are perpendicular to each other. Order of wavelength in electromagnetic spectrum Cosmic rays < l-rays < X-rays < Ultraviolet rays < Visible < Infrared < Micro waves < Radio waves. Plank’s Quantum Theory: Some important phenomena such as interference and diffraction are generally explained by wave nature of electromagnetic radiation..
62. Atomic Structure (i) Nature of emission of radiation from the surface of hot bodies (black - body radiation) (ii) Ejection of electrons from the surface of metal happens when radiation strikes it (photoelectric effect) Photoelectric Effect (P.E.E.): The ejection of electrons when light of certain minimum frequency called as threshold frequency is incident on a matel surface is called as photoelectric effect. Incident energy = Work function (φ) + K.K.max¬ Ei = φ + (K.E.)max hn = hn0 + (1/2) mev2 where me is mass of electron and v is the velocity associated with the ejected electron. Bohr’s Atomic Model: Energy of an electron remains constant as long as it stays in same orbit called stationary Orbit. A fixed amount of energy is associated with each stationary orbit and hence it is called Energy level. Energy of an electron: T E P E K E. . . . . . 2 T E Z n eV atom. . . / 13 6 2 2 Ground state (G.S.): In any single electron species n = 1 is called ground state. Excited state (E.S.): In single electron species n > 1 is called excited state. For the nth shell = (n - 1) the excited state Excitation energy: Energy required to excite an electron from its ground state to any excited state is called excitation energy. Wave Mechanical Model of An Atom: WAVE MECHANICAL MODEL OFAN ATOM: The Dual Nature of Matter (The Wave Nature of Electron) De-Broglie Equation (Dual nature of matter and radiation): h mc h p h mv h m K E2 ( . .) If a charged particle Q is accelerated through potential difference V from rest then De-broglie wavelength is h mQV2
63. Atomic Structure The circumference of the nth orbit is equal to n times the wavelength of the electron. 2prn = nl. Heisenberg’s Uncertainity Principle: It is impossible to obtain simultaneously both position and velocity (or momentum) of a microscopic particle with absolute accuracy. x p h or m x v h or x v h m . . . 4 4 4 Quantum Mechanical Model: The Schrodinger Equation: 2 2 2 2 2 2 2 2 2 2 2 8 8 0 x y z m h or m h E V ( ) Quantum Numbers: (i) Principal quantum number (n): Number of orbitals present in nth shell = n2. The maximum number of electrons which can be present in a principal energy shell is equal to 2n2. (ii) Azimuthal quantum number (l): Number of orbitals in a given subshell = 2l + l Maximum number of electrons in particular subshell = 2 × (2l + l) Orbital angular momentum L h 2 1 1 ℏ ( ) ( ) (iii) Magnetic quantum number (m): It describes the orientations of the subshells. It can have values from –l to +l including zero, i.e., total (2l + l) values. (iv) Spin quantum number (s): It describes the spin of the electron. It has values +1/2 and –1/2. (+) signifies clockwise spinning and (–) signifies anticlockwise spinning. Shape of The Orbitals: Nodal plane and Nodal surface :- The space where probability of finding an e– is zero. Nodal plane = l ; Nodal surface = n - l – 1 Stability of Completely Filled and Half-filled Subshells: Symmetrical distribution of electrons: Due to small shielding, the electrons are pulled closer to the nucleus and this decrease in energy leads to stability. Exchange energy: Electrons with the same spin have a tendency to exchange their positions when they are present in the degenerate orbitals of a subshell. The energy released during this exchange is called exchange energy