Atoms Class 12 Notes | Term 2 | Physics |

Distance of Closest Approach At a certain distance r₀ from the nucleus, whole of the KE of α-particle converts into electrostatic potential energy and α-particle cannot go farther close to nucleus, this distance (r₀) is called distance of closest approach.

Drawbacks of Rutherford’s Model
(i) Could not explained stability of atom clearly.
(ii) Unable to explain line spectrum.

BOHR’S MODEL OF HYDROGEN ATOM

• Drawbacks of Rutherford’s atomic model lead to the Bohr’s Model where he came up with 3 postulates:
• First  Postulate : Atoms have some specific stable energy states(called stationary states) where electrons could orbit around the nucleus without emitting radiation
• Second Postulate: Orbiting of electrons occur only in the orbits (called stable orbits) where electrons’ angular momentum(L) is equal to the integral multiples ofh/(2π), leading to the quantization of moving electron

          L_N =MV_NR_N = NH/(2Π)

Here    h= Planck’s constant = 6.6×10^-34Js

L_n= angular momentum of electron in n^th orbit

v_n= velocity of electron in n^th orbit

r_n= radius of n^th orbit

n= permitted orbits on which electron revolve (called principle quantum number)

• Third Postulate: Electron while jumping from higher(initial) energy state to lower(final) energy state, emit a photon of energy equal to the energy difference between the 2 energy states, and its frequency is given by:

hv = E_i – E_f

Bohr’s Radius: The radius on which electron move around the nucleus in the orbit described by the Bohr’s model is known as Bohr’s radius.

Using the second postulate and Rutherford’s model(eq.1)

mvr = nh/(2π)

Using the value of υ²from both the equations, we get

On solving (and putting Z=1 for hydrogen atom) we get:

r = n²h²Ɛ_o/(πme²)

For radius of innermost orbit, put n=1

 

Velocity of Electron in the Orbit

v = e²/2nhƐ_o

 Limitations of Bohr’s Model
(i) Applicable only for hydrogen like atom.
(ii) Does not explain the fine structure of spectral lines in H-atom.
(iii) Does not explain about shape of orbit.

ATOMIC SPECTRA

• When an electron jumps amongst energy levels in an atom, energy is emitted or absorbed in the form of electromagnetic radiations and these radiations produce a spectral lines of frequencies(or wavelength) associated with an atom, called atomic spectra
• Spectroscopy is the learning and examination emission and absorption spectra associated with an atom to determine its properties
• Spectral lines are the bright and dark line series that constitute the spectrum associated with an atom
• An atom has a discrete spectra(where exist a fixed specific lines of energy transition of electron with discrete energy gaps) also known as quantized spectra
• Another type is continuous spectra(where there is no specific lines of energy transition of electrons) which is the reverse of discrete spectra

• There are 3 types of atomic spectra: a)emission spectra, b)absorption spectra, c) continuous spectra

Emission Spectra

• Radiation spectrum produced due to absorption of energy by a matter
• When an electron of an atom, molecules or ions get to a higher energy state than their ground (stable) state due to radiation absorption, they are said to be excited
• Emission spectrum is produced when energy is supplied to a sample (through heating or irradiation) and the wavelength or frequency of radiation emitted by the sample is observed as a function of energy

Absorption Spectra

• It is just the opposite of emission spectra
• Continuous radiation (energy) is directed through a sample which absorbs certain radiation of particular wavelengths and the remaining spectrum is recorded. Absorbed wavelengths correspond to the dark spaces in the spectrum
• Whatever absent(showed by dark lines) in the emission spectrum of an atom is actually present (showed by bright lines) in the absorption spectrum of that atom

Continuous Spectra

• Formed when a ray of white light is passed through a prism(or water droplets) causing a continuous spectrum of visible light of different wavelength
• There are no discrete lines (separation) between any 2 adjacent wavelengths
• Speed of light changes with respect to the medium through which it passes, so as the medium changes, light with the longest wavelength (red)deviates the least and the light with the shortest wavelength (violet) deviates the most

SPECTRAL SERIES

• On passing electric discharge through hydrogen gas, hydrogen molecules would dissociate giving rise to excited (highly energetic) hydrogen atoms that emit radiation of certain specified frequency while returning to its ground state
• Hydrogen spectra is constituted of 5 series of spectrum named after their discoverer(Lyman, Balmer, Paschen, Bracket and Pfund series)