A moving hydrogen atom absorbs a photon of wavelength 221 nm and stops. If the mass of the hydrogen atom is $1.67 × 10^{-27} kg$, what will be the linear momentum of the photon? (Given: $h = 6.63 × 10^{-34} Js$)
Answer & explanation
Correct answer: option 3
The correct answer is Option (4) → $3 × 10^{-27}kg\, m\, s^{-1}$
The linear momentum of a photon is related to its wavelength by the formula:
$P_{\text{photon}} = \frac{h}{\lambda}$
Here, $h$ is Planck's constant ($6.63 \times 10^{-34} \, \text{Js}$) and $\lambda$ is the wavelength of the photon.
Given $\lambda = 221 \, \text{nm} = 221 \times 10^{-9} \, \text{m}$,
$P_{\text{photon}} = \frac{6.63 \times 10^{-34}}{221 \times 10^{-9}}$
$P_{\text{photon}} \approx 2.998 \times 10^{-27} \, \text{kg·m/s}$
Rounding to one significant figure in standard form,
$P_{\text{photon}} \approx 3 \times 10^{-27} \, \text{kg·m/s}$
This is the momentum carried by the photon that stops the hydrogen atom upon absorption.