Using Bohr’s postulates, obtain the expression for the total energy of the electron in the stationary states of the hydrogen atom. Hence draw the energy level diagram showing how the line spectra corresponding to Balmer series occur due to transition between energy levels.
According to Bohr’s postulates, in a hydrogen atom, a single electron revolves around a nucleus of charge +e. For an electron moving with a uniform speed in a circular orbit on a given radius, the centripetal force is provided by the Coulomb force of attraction between the electron and the nucleus.
Therefore, 
... (1)
Potential energy is given by,
P.E = 
Therefore, total energy is given by,
E = K.E + P.E = 
For nth orbit, E can be written as En,
... (2)Now, using Bohr's postulate for quantization of angular momentum, we have
Putting this value of v in equation (1), we get
The ground state energy of hydrogen atom is – 13.6 eV. If an electron makes a transition from an energy level – 0.85 eV to –3.4 eV, calculate the wavelength of the spectral line emitted. To which series of hydrogen spectrum does this wavelength belong?
Using the formula,
For, n=1; E1 = - 13.6 eV
During the electron transmission, EA = - 0.85 eV to EB = -3.4 eV
So, from equation (i), we have
Therefore, electron transition takes place from n=4 to n=2 which corresponds to Balmer series.
We know,
Here,
nA = 4 ; nB = 2 ; R = 1.097 x 107 m-1
Then, 
Using Rutherford model of the atom, derive the expression for the total energy of the electron in hydrogen atom. What is the significance of total negative energy possessed by the electron?
OR
Using Bohr’s postulates of the atomic model derive the expression for radius of nth electron orbit. Hence obtain the expression for Bohr’s radius.According to Rutherford’s model, we have
Energy is negative implies that the electron–nucleus is a bound or attractive system.
OR
According to the Bohr’s atomic model, electrons revolve around the nucleus only in those orbits for which the angular momentum is an integral multiple of 
.
So, as per Bohr’s postulate, we have
This is the required expression for Bohr's radius.
Bohr's Quantisation Rule:
According to Bohr, an electron can revolve only in certain discrete, non-radiating orbits for which the total angular momentum of the revolving electron is an integral multiple of 
; where h is the Planck's constant.
That is, 
b)
Using Rydberg's formula for spectra of hydrogen atom, we have
Hence, the relation between 3 wavelengths from the energy-level diagram is obtained.
In a Geiger–Marsden experiment, calculate the distance of closest approach to the nucleus of Z =80, when an a-particle of 8 MeV energy impinges on it before it comes momentarily to rest and reverses its direction.
How will the distance of closest approach be affected when the kinetic energy of the a-particle is doubled?
Let ro be the distance of closest approach where the kinetic energy of the alpha-particle is converted into it’s potential energy.
Given, Z = 80, Ek = 8 MeV
Since, 
Kinetic energy of the particle becomes doubled if the distance of closest approach becomes half.
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