Q. When an electron jumps from a level n = 4 to n = 1, the momentum of the recoiled hydrogen atom will be

(a) 6.5 × 10^{-27} kg ms^{-1 }

(b) 12.75 × 10^{-19} kg ms^{-1}

(c) 13.6 × 10^{-27} kg ms^{-1 }

(d)zero

Ans: (a)

Sol: Momentum of recoiled hydrogen atom , P = h/λ

$\large \frac{1}{\lambda} = R Z^2 [\frac{1}{n_1^2} – \frac{1}{n_2^2}]$

For hydrogen , Z = 1

$\large \frac{1}{\lambda} = R [\frac{1}{n_1^2} – \frac{1}{n_2^2}]$

As , P = h/λ

$\large P = h R [\frac{1}{n_1^2} – \frac{1}{n_2^2}]$

$\large P = 6.6 \times 10^{-34} \times 10^7 [\frac{1}{1^2} – \frac{1}{2^2}]$

= 6.5 × 10^{−27} Kg m/s