A particle of mass \(9.1 \times 10^{-31}\, {kg}\) travels in a medium with a speed of \(10^{6}\, {m} / {s}\) and a photon of a radiation of linear momentum \(10^{-27} \,{kg}\, {m} / {s}\) travels in vacuum. The wavelength of photon is \(....\) times the wavelength of the particle.

\(\therefore\) For particle,

\(\lambda_{ pa }=\frac{h}{m v}=\frac{6.6 \times 10^{-34}}{9.1 \times 10^{-31} \times 10^{6}}\)

and for photon,

\(\lambda_{ ph }=\frac{h}{p}=\frac{6.6 \times 10^{-34}}{10^{-27}}\)

From Eqs. (i) and (ii), we get

\(\Rightarrow \quad \frac{\lambda_{ ph }}{\lambda_{ pa }}=\frac{\frac{6.6 \times 10^{-34}}{10^{-27}}}{\frac{6.6 \times 10^{-34}}{9.1 \times 10^{-31} \times 10^{6}}}\)

\(\Rightarrow \quad \frac{\lambda_{ ph }}{\lambda_{ pa }}=910\)

\(\Rightarrow \quad \lambda_{ ph }=910\left(\lambda_{ pa }\right)\)