Question:
A particle of mass $9.1 \times 10^{-31} \mathrm{~kg}$ travels in a medium with a speed of $10^{6} \mathrm{~m} / \mathrm{s}$ and a photon of a radiation of linear momentum $10^{-27} \mathrm{~kg} \mathrm{~m} / \mathrm{s}$ travels in vacuum. The wavelength of photon is times the wavelength of the particle.
Solution:
For photon $\lambda_{1}=\frac{\mathrm{h}}{\mathrm{P}}=\frac{6.6 \times 10^{-34}}{10^{-27}}$
For particle $\lambda_{2}=\frac{\mathrm{h}}{\mathrm{mv}}=\frac{6.6 \times 10^{-34}}{9.1 \times 10^{-31} \times 10^{6}}$
$\therefore \frac{\lambda_{1}}{\lambda_{2}}=910$
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