Question

Electrons of energies $10.2eV$ colliding with a hydrogen atom cause radiation to be emitted from the latter. What is the wavelength of radiation in terms of Rydberg's constant $R$ if the ground state energy of the atom is $-13.6eV$?

• A. $\frac{4}{3R}$
• B. $\frac{1}{3R}$
• C. $\frac{5}{3R}$
• D. $\frac{1}{5R}$

Answer 1

The correct option is A $\frac{4}{3R}$

Ground state energy $=-13.6eV[\therefore z=1,n=1]$
Energy of colliding electron $=10.2eV$
New energy state $=-13.6eV+10.2eV$
$=-3.4eV$

It is transferred to $2^{nd}$ orbit, $n=2$
$\frac{1}{\lambda }=R\times 1^2\times [\frac{1}{1^2}-\frac{1}{2^2}]$
$\lambda =\frac{4}{3R}$