Atomic Physics At-A-Glance

Key Terms

• Discharge tube: A glass tube which encloses a rarified gas at a very low pressure of 10-3 cm. of Hg. The cathode and anti cathode are connected through a high voltage.
  
• Cathode rays: Cathode emits invisible radiation streaming away from it and produce scintillations on fluorescent material and are Cathode rays
  
• Electron: Electron was thus discovered during experiments on the discharge of electricity through rarified gases.
  
• The magnitude of electric charge (e) was determined by Millikan Charge of the electron  =   1.602 x 10 ^-19 coulomb
• X-Rays:  Invisible electromagnetic radiations. Wavelengths range form 0.010A0 – 100A0. These are discovered by Roentgen.

Atomic Physics

• Discovery and properties of electrons
  
• The Bohr’s theory and atomic spectra
  
• X-Rays
  
• Wave nature of matter
  
• de Broglie hypothesis
  
• Heisenberg's uncertainty principle

Discovery and propertiesof electrons

• Discovery - 1897 J.J.Thomson
• 
  
• The magnitude of electric charge (e) was determined by Millikan. Charge of the electron  =   1.602 x 10 ^-19coulomb
  
• Specific charge of electron (i.e., ratio of charge to mass) was determined by Thomson  e / m of  the electron = 1.76   X  10¹¹ coulomb/kg
  
• Electrons can be obtained by number of methods
  
• Discharge of electricity this gases,
  
• Thermionic emission
  
• Photoelectric effect

Bohr’s atom model - atomic spectra

• Bohr’s atom model - Proposed by Neil Bohr in 1913
  
• Bohr applied the Planck’s quantum theory to the Rutherford nuclear atom with remarkable success.
  
  
• First postulate:  An atom consists of a positively charged nucleus at the centre. The electrons move round the nucleus in certain stationary orbits of definite radii and not all possible radii.
  
• Second postulate:  The radius of the orbit is such that the angular momentum of the electron is an integral multiple of h/2p
  
  • m =  mass of the electron - V is the velocity of the electron - r is the radius of the orbit - h is Planck’s constant - I is moment of inertia  - w is angular velocity of the electron - n is an integer n = 1,2,3,4,5…..
    
  • The angular momentum mvr = nh/2p
    
  • While revolving around these stationary orbits, the electrons do not emit any Electromagnetic radiation.The total energy of the electron remains constant.
    
• Third postulate: Electron may jump from one orbit to the other, in which case the difference in energy between the two states of motion is radiated in the form of a light quantum.
  
  • This is called  Bohr’s frequency condition
    
  • The Coulombian and Newtonian forces are applicable in the region of the atom -
  • Centripetal force = Electrostatic force of attraction
    
  • The velocity of electrons in the first Bohr orbit of the atom is  1/137  times the velocity of light. These orbits are called stationery orbits.
    
  • For an electron of charge, ‘e‘, mass ‘m‘ to revolve around a nucleus of charge ‘z e‘ in a circular orbit of radius ‘r
    
  • Bohr noted that Planck’s constant h, had the units of angular momentum  L = mvr
  • kgm2/sec = joule-sec
    
  • He has taken L = n h  and quantized angular momentum
    
  • Actually, what he needed was this: L = n (h/2p  ) =n h
    
  • where h = h/2p, From V, r, E, L
    
  • The radius of the orbit is
    r  = n2 h 2 / (me z e2) = (5.3 x 10-11 m)  X  n2
    
  • The radius of each orbit in an atom is fixed and thus the concept of Stationary orbits was established
    
  • The energy of the electron in the orbit is
    
  • E = [ -me z2 e4 / 2 h2 ] X ( 1/n2 ) =  -13.6 eV / n2
    
  • where 1 eV = 1.6 x 10^-19 Joules
    
  • for n=1            E =  -13.6 eV
    
  • When an electron changes its energy state it can do so only from one allowed state to another allowed state
    
  • DE = hf = [-13.6 eV] X [(1/ni2) - (1/nf2)]
  • Energy of the electron  - discrete values : -13.6eV, -3.40eV, -1.51eV,  -0.85eV  - establishes the quantization of Bohr orbits

Atomic Spectra
Solids, liquids and diffused gases emit light when heated.
This light when allowed to pass through a prism, spectroscope etc. produce ordered arrangement of lines or bands or continuous patch of light. This is called spectrum.
The spectrum of excited gases contains ordered arrangement of bright lines separated by dark spaces.
This is called emission line spectrum.
The spectrum of sun’s light is called solar spectrum
This is continuous spectrum crossed by dark lines.is called absorption line spectrum. The line spectrum is emitted by matter in the atomic state. The line spectrum serves as a key to the structure of the atom.
Any theory on the structure of the atom should be able to explain the emission of line spectrum
The Bohr theory accurately predicts the ionization energy for hydrogen as 13.6eV
The value of ‘R’ was estimated  as 1.097 X 10⁸ m-1
It gives a model for why atoms emit line spectra
It also accounts for the absorption spectra
de Broglie ‘s hypothesis explains why orbits are quantized in Bohr’s theory of atom model
According to De Broglie a particle of mass ‘m’ moving with a speed ‘v’ would have a wavelength
λ = h / m v.        ldeBroglie = h / mv = h / p

Wave partivle duality

•                or                         
  
• De Broglie hypothesis: Photons are treated as “packets of light” behaving like a particle.
  
• Momentum  of a photon  p = E / c = hl
  
• Energy of a photon       E = hc/l
  
• To understand any given experiment, we must use either the wave or the photon theory, but not both.
  
• Light sometimes behaves like a wave and some times like a particle
  
• According to de Broglie - Electrons and other material objects might also have wave properties.

Heisenberg’s uncertainty principle

• If position is identified the momentum cannot be measured
  
• If momentum is measured the position is lost.
  
• Dx  X  Dp ³ h / 2
  
• This is a mathematical form of Heisenberg’s uncertainty principle

X-Rays

• X-Rays :  Invisible  electromagnetic  radiations, Wavelengths range form 0.010A – 100A0. These are discovered by Roentgen.
  
• Origin:  When a fast moving electron is suddenly stopped a part of its kinetic energy is converted into X-ray photonthe rest of the energy is converted into heat.
  
  
• The maximum frequency of x-rays produced by an X-rays tube is given by fmax = eV/ h  or lmin = c h/eV
  
• X-rays are electromagnetic waves with wavelengths ranging from 100A0 to 1 / 100 A0.
  
• Continuous X- ray spectrum: Produced   during the direct conversion of a part of the K.E. of the   electron into X-ray photon.
  
• Characteristic X- ray spectrum: At a high operating potential electron that strikes the anode knocks out one of the K-electrons of target atom. These X-ray photons have specific wavelengths and give rise to characteristic X –ray spectrum (K-series) and L-series of spectral lines.
  
• Moseley’s Law: The frequency of a spectral line in the characteristic spectrum of X-rays is related to the atomic number of the atom
  Öf =  a(z-b) where a and b are constants
  
• Discovery of New elements