Question

An electron and a photon have same wavelength. If $p$ is the momentum of electron and $E$ is the energy of photon, the magnitude of $p/E$ in $SI$ unit is

• A. $3.0\times {10}^8$
• B. $3.33\times {10}^{-9}$
• C. $9.1\times {10}^{-31}$
• D. $6.64\times {10}^{-34}$

Answer 1

Answer: (B)

$3.33\times {10}^{-9}$

From DeBroglie relation

$\lambda =\frac{h}{p}$

and using energy relation

$E=\frac{hc}{\lambda }$ or

$\lambda =\frac{hc}{E}$

Equating these two

$\frac{h}{p}=\frac{hc}{E}$

hence , $\frac{p}{E}=\frac{1}{c}=3.33\ast {10}^{-9}$