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  • A particle of mass  travels in a medium with a speed of and a photon of a radiation of linear momentum

A particle of mass 9.1\times 10^{-31} 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.
 

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\begin{aligned} &m=9.1 \times 10^{-31} \mathrm{~kg} \\ &V=10^{6} \mathrm{~m} / \mathrm{s} \end{aligned}

\begin{gathered} \text { Momentum of photon }=P=10^{-27} \mathrm{~kg}\left(\frac{\mathrm{m}}{\mathrm{s}}\right) \\ \qquad \begin{array}{c} P=\frac{h}{\lambda}=10^{-27} \\ \lambda_{\text {photon }}=\frac{h}{10^{-27}} \rightarrow(1) \end{array} \end{gathered}

\lambda_{\text {clectron }}=\frac{h}{mv}=\frac{h}{9.1 \times 10^{-25}} \rightarrow(2)

\begin{aligned} &\frac{\lambda_{\text {photon }}}{\lambda_{\text {electron }}}=\frac{h / 10^{-27}}{h / 9.1 \times 10^{-25}} \\ &\frac{\lambda_{\text {photon }}}{\lambda_{\text {electron }}}=\frac{9.1 \times 10^{-25}}{10^{-27}}=910 \end{aligned}

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vishal kumar

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