Physics

Problem

A free hydrogen atom after absorbing a photon of wavelength

\lambda_a

gets excited from the state

n=1

to the state

n=4

. Immediately after that the electron jumps to

n=m

state by emitting a photon of wavelength

\lambda_e

. Let the change in momentum of atom due to the absorption and the emission are

\Delta p_a

and

\Delta p_e

, respectively. If

\lambda_a / \lambda_e = \frac{1}{5}

, which of the option(s) is/are correct? [Use

hc = 1242

eV nm;

1 \text{ nm} = 10^{-9} \text{ m}

h

and

c

are Planck's constant and speed of light, respectively] a.

\Delta p_a / \Delta p_e = \frac{1}{2}

b. The ratio of kinetic energy of the electron in the state

n=m

to the state

n=1

\frac{1}{4}

m=2

\lambda_e = 418 \text{ nm}