Title 12. ATOMS.pdf ✅

Various Models For Structure Of Atom Dalton’s Theory Every material is composed of minute particles known as atom. Atom is indivisible i.e. it cannot be subdivided. It can neither be created nor be destroyed. All atoms of same element are identical (Physically as well as chemically), whereas atoms of different elements are different in properties. The atoms of different elements are comparable to hydrogen atoms. (The radius of the heaviest atom is about 10 times that of hydrogen atom and its mass is about 250 times that of hydrogen). The atom is stable and electrically neutral. Thomson’s Atom Model The atom as a whole is electrically neutral because the positive charge present on the atom (sphere) is equal to the negative charge of electrons present in the sphere. Atom is a positively charged sphere of radius 10–10 m. in which electron are embedded in between. The positive charge and the whole mass of the atom is uniformly distributed throughout the sphere. Shortcomings of Thomson’s model (i) The spectrum of atoms cannot be explained with the help of this model. (ii) Scattering of -particles cannot be explained with the help of this model. Rutherford experiments on scattering of -particles by thin gold foil The experimental arrangement is shown in figure. -particles are emitted by some radioactive material (polonium), kepi inside a thick lead box. A very fine beam of a-particles pass through a small hole in the lead screen. This well collimated beam is then allowed to fall on a thin gold foil. While passing through the gold foil, -particles are scattered through different angles. A zinc sulphide screen was placed on the other side of the gold foil. This screen was movable, so as to receive the a-particles, scattered from the gold foil at angles varying from 0° to 180°. When an - particle strikes the screen, it produces a flash of light and it is observed by the microscope. It was found that : (i) Most of the -particles went straight through the gold foil and produced flashes on the screen as if there were nothing inside gold foil. Thus, the atom is hollow. (ii) Few particles collided with the atoms of the foil which have scattered or deflected through considerable large angles. Few particles even turned back towards source itself. (iii) The entire positive charge and almost whole mass of the atom is concentrated in small center called a nucleus. (iv) The electrons could not deflect the path of a -particles i.e., electrons are very light. CHAPTER – 12 ATOMS ATOMS
(v) Electrons revolve round the nucleus in circular orbits. So, Rutherford 1911, proposed a new type of model of the atom. According to this model, the positive charge of the atom, instead of being uniformly distributed throughout a sphere of atomic dimension is concentrated in a very small volume (Less than 10–13 cm is diameter) at it center. This central core, now called nucleus, is surrounded by clouds of electron makes the entire atom electrically neutral. According to Rutherford scattering formula, the number of -particle scattered at an angle e by a target are given by Nθ = N0nt(2 Ze2) 2 4(4πε0) 2r 2(mv0 2) 2 × 1 sin4θ 2 Where N0 = number of -particles that strike the unit area of the scatter n = number of target atom per m3 t = thickness of target Ze = charge on the target nucleus 2e = charge on -particle r = distance of the screen from target v0 = initial velocity of -particles Now closest approach distance is (r0) = 1 4πε0 × (2 Ze) 2 [ 1 2 mv0 2] = 1 4π∈0 (2Ze) 2 EK Where EK = K.E. of -particle Failure of Rutherford's Atomic model: (i) It couldn't explain the stability of atom. (ii) It couldn't explain discrete nature of hydrogen spectra. Bohr's Theory Of Hydrogen Atom Bohr's theory of hydrogen atom is based on the following assumption An electron in an atom moves in a circular orbit about the nucleus under the influence of coulomb's force of attraction between the electron and nucleus As the atom as a whole is stable the coulombian force of attraction provides necessary centripetal force: e 2 4πε0r 2 = mv 2 r .....(i) Only those orbits are possible for which the angular momentum of the electron is equal to an integral multiple of h 2π i.e. mvr = n h 2π .....(ii) Where h is Planck’s constant. The electron moving in such allowed orbits does not radiate electromagnetic radiations. Thus, the total energy of the electron revolving in any of the stationary orbits remains constant. Electromagnetic radiations are emitted if an electron jumps from stationary orbit of higher energy E2 to another stationary orbit of lower energy, E1. The frequency v of the emitted radiation is related by the equation. E2 – E1 = hv .... (iii) Shortcomings of Bohr's model This model could not explain the fine structure of spectral lines, Zeeman effect and Stark effect. This model is valid only for single electron systems. (Cannot explain electron-electron interaction) This model is based on circular orbits of electrons whereas in reality there is no orbit. Electron is presumed to revolve round the nucleus only whereas in reality motion of electron cannot be described. This model could not explain the intensity of spectral lines. It could not explain the doublets obtained in the spectra of some of the atoms. Bohr’s model is semi quantum model, it means, it includes two quantum numbers (E and L) but unfortunately it considers circular motion of electron. Characteristics Of Bohr Model Radii Of Orbits From equation v = nh 2πmr , Here n is number of orbits Substituting value of v in equation e 2 4πε0r 2 = m r [ nh 2πmr] 2  r = mn 2h 2 .4πε0r 2 4π2m2r 2e 2 = n 2h 2 ε0 πme 2 In general, rn = n 2h 2ε0 πme 2 .... (iv) equation (iv) shows that the radii of the permitted orbits vary as the square of n. For the smallest orbit n = 1substituting the values of h, 0, m and e we have radius of first orbit r1 = 0.529 × 10–10m = 0.529 Å Q. In the Bohr model of a hydrogen atom, the centripetal force is furnished by the coulomb attraction between the proton and the electron. If a0 is the radius of the ground state orbit, m is the mass and e is the charge on the electron and e0 is the vacuum permittivity, then determine the speed of the electron. Sol. Centripetal force = force of attraction of nucleus on electron mv 2 a0 = 1 4πε0 e 2 a0 2 ⇒ v = e √4πε0a0m

subjected to external energy, the electron jumps from lower energy State i.e., the hydrogen atom is excited. The excited state is not stable hence the electron returns to its ground state in about 10–8 seconds. The excess of energy is now radiated in the form of radiations of different wavelength. The different wavelength constitutes spectral series. Which is characteristic of atom emitting, then the wavelength of different members of series can be found from the following relations. This relation explains the complete spectrum of hydrogen. A detailed account of the important radiations is listed below. Lyman Series: The series consist of wavelength which are emitted when electron jumps from an outer orbit to the first orbit i.e., the electron jumps to K orbit give rise to Lyman series. Here n1 = 1 and n2 = 2, 3, 4, ....... . Balmer Series This series is consisting of all wavelengths which are emitted when an electron jumps from an outer orbit to the second orbit i. e. the electron jumps to L orbit give rise to Balmer series. Here n1 = 2 and n2 = 3, 4, 5 .........  Paschen Series This series consist of all wavelengths are emitted when an electron jumps from an outer orbit to the third orbit i.e., the electron jumps to M orbit give rise to Paschen series. Here n1 = 3 and n2 = 4, 5, 6 .......  Brackett Series This series is consisting of all wavelengths which are emitted when an electron jumps from an outer orbit to the fourth orbit i.e., the electron jumps to N orbit give rise to Brackett series. Here n1 = 4 and n2 = 5, 6, 7, ......  Pfund series The series consist of all wavelengths which are emitted when an electron jumps from an outer orbit to the fifth orbit i.e., the electron jumps to O orbit give right to Pfund series. Here n1 = 5 and n2 = 6, 7, 8 .........  De Broglie’s Explanation Of Bohr’s Second Postulate Of Quantization De Broglie came up with an explanation for why the angular momentum might be quantized in the manner Bohr assumed it was. De Broglie realized that if you use the wavelength associated with the electron, and assume that an integral number of wavelengths must fit in the circumference of an orbit, you get the same quantized angular momenta that Bohr did. The circumference of the circular orbit must be an integral number of wavelengths: 2πr = nλ = nh p (λ = h p ) The momentum, p, is simply mv as long as we're talking about non-relativistic speeds, so this becomes: 2πr = nh mv Rearranging this a little gives the Bohr relationship: Lr = mvr = nh 2π 2 2 1 2 1 1 1 v R n n   = = −      Q. An electron makes a transition from orbit n = 4 to the orbit n = 2 of a hydrogen atom. What is the wavelength of the emitted radiations? (R = Rydberg’s constant) Sol. Transition of hydrogen atom from orbit n1 = 4 to n2 = 2. Wave number = 1 λ = R [ 1 n1 2 − 1 n2 2 ] = R [ 1 (2) 2 − 1 (4) 2 ] = R [ 1 4 − 1 16] = R [ 4−1 16 ] = 3R 16 ⇒ λ = 16/3R Q. Ionization potential of hydrogen atom is 13.6 eV. Hydrogen atoms in the ground state are excited by monochromatic radiation of photon energy 12.1 eV. According to Bohr’s theory, the which spectral lines will be emitted by hydrogen. Sol. Ionization potential of hydrogen atom is 13.6 eV. Energy required for exciting the hydrogen atom in the ground state to orbit n is given by E = En − E1 i.e., 12.1 = − 13.6 n2 − ( −13.6 1 2 ) = − 13.6 n2 + 13.6 or, −1.5 = −13.6 n2 or, n 2 = 13.6 1.5 = 9 or, n = 3 Number of spectral lines emitted = n(n−1) 2 = 3×2 2 = 3