A photon has a momentum of $3.3 × 10^{-29}\, kg\, m/s$. The frequency of the waves associated with the photon will be
(Given: $h= 6.6 × 10^{-34} Js$)
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → $1.5 × 10^{13}\, Hz$
Given: Photon momentum $p = 3.3 \times 10^{-29}\,\text{kg·m/s}$
For a photon, $p = \frac{h}{\lambda} \Rightarrow \lambda = \frac{h}{p}$
Planck's constant: $h = 6.626 \times 10^{-34}\,\text{J·s}$
Wavelength: $\lambda = \frac{6.626 \times 10^{-34}}{3.3 \times 10^{-29}} \approx 2.008 \times 10^{-5}\,\text{m}$
Frequency: $f = \frac{c}{\lambda}$, $c = 3 \times 10^8\,\text{m/s}$
$f = \frac{3 \times 10^8}{2.008 \times 10^{-5}} \approx 1.49 \times 10^{13}\,\text{Hz}$
Answer: $f \approx 1.49 \times 10^{13}\,\text{Hz}$