An electron collides with a fixed hydrogen atom in its ground state. Hydrogen atom gets excited and the colliding electron loses all its kinetic energy. Consequently the hydrogen atom may emit a photon corresponding to the largest wavelength of the Balmer series. The minimum K.E. of colliding electron will be

Options

A. 10.2 eV
B. 1.9 eV
C. 12.1 eV
D. 13.6 eV

Answer

C

Explanation

Excitation up to n=3 is required so that visible length is emitted upon de-excitation.
`E_1 = (-13.6)/(1^2) , " "E_2=(-13.6)/9`
`:. E_2-E_1=(-13.6)/9 +(13.6)/1`
So required energy `= 13.6 (1-1/9) = 12.1 eV`