Question

An electron and a photon have same wavelength of $10^{-9}\, m$. If $E$ is the energy of the photon and $p$ is the momentum of the electron, then the magnitude of $E / p$ (in SI unit) is

• A. $1.00$ x$ 10^{-9}$
• B. $1.50$ x $10^8$
• C. $3.00$ x $10^8$
• D. $1.20$ x $10^7$

Answer 1

Answer: (C)

For a photon energy is
$E=hf=\frac{hc}{\lambda}$
For an momentum of electron is $P=\frac{h}{\lambda}$
So, $\frac{E}{p}=\frac{hc/ \lambda}{h / \lambda} =c$
here, $\lambda$ is same for both photon and electron.
$\Rightarrow \frac{E}{P}=3\times10^{8}ms^{-1}$