If the de Broglie wavelength of an electron i | vedclass

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(D) The de Broglie wavelength of an electron is given by $\lambda_e = \frac{h}{mv}$.The wavelength of a photon is given by $\lambda_p = \frac{c}{
u}$

Vedclass · Accepted Answer

$1.45 	imes 10^6 \, m/s$

Vedclass · Answer

(D) The de Broglie wavelength of an electron is given by $\lambda_e = \frac{h}{mv}$.The wavelength of a photon is given by $\lambda_p = \frac{c}{
u}$,where $
u$ is the frequency.According to the problem,$\lambda_e = 10^{-3} 	imes \lambda_p$.Substituting the expressions: $\frac{h}{mv} = 10^{-3} 	imes \frac{c}{
u}$.Rearranging for the speed of the electron $(v)$: $v = \frac{h 
u}{m c 	imes 10^{-3}}$.Substituting the given values: $v = \frac{6.63 	imes 10^{-34} 	imes 6 	imes 10^{14}}{9.1 	imes 10^{-31} 	imes 3 	imes 10^8 	imes 10^{-3}}$.$v = \frac{39.78 	imes 10^{-20}}{27.3 	imes 10^{-26}} = 1.457 	imes 10^6 \, m/s \approx 1.45 	imes 10^6 \, m/s$.

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