Derive an expression for the radius of n^th Bohr’s orbit in Hydrogen atom.

OR

Energy of electron in first excited state in Hydrogen atom is -3.4eV. Find KE and PE of electron in the ground state.

According to Bohr’s model, the electron revolves revolve in stationary orbits where the angular momentum of electron is an integral multiple of h/2π.

_______________ (1)

Here, h is Planck's constant.

Now, when an electron jumps from an orbit of higher energy E2 to an orbit of lower energy E1, it emits a photon. The energy of the photon is E2-E1. The relation between wavelength of the emitted radiation and energy of photon is given by the Einstein - Planck equation.

E2-E1= hf ____________ (2)

For an electron of hydrogen moving with a constant speed v along a circle of radius R with the center at the nucleus, the force acting on the electron according to Coulomb’s law is:

The acceleration of the electron is given by v2/r. If m is the mass of the electron, then according to Newton’s law:

F=ma

_______________ (3)

From equation (1) and (3) we get,

For nth orbit,

OR

The K.E is equal to the (-) ve of the energy of the electron and P.E is equal to twice of the energy of the electron.

K.E in ground state =

P.E in ground state =2× (-13.6) =-27.2eV