Question

An electron and a photon have the same wavelength of ${10}^{-9}\text{m}$. If E is the energy of the photon and p is the momentum of the electron, the magnitude of $E/P$ in SI units is?
(A) $1.00\times {10}^{-9}$
(B) $1.50\times {10}^8$
(C) $3.00\times {10}^8$
(D) $1.20\times {10}^7$

Answer 1

Hint: Initially you must be aware of the general formula of momentum and photon. De-Broglie wavelength plays an important factor in this question. Deriving a relation between energy and momentum by wavelength will surely help you.

Complete step by step solution:
Given:
$\lambda ={10}^{-9}\text{m}$
Formula:
$E={\displaystyle \frac{hc}{\lambda }}$
Calculation:
 From Planck's equation
$\Rightarrow$ $E={\displaystyle \frac{hc}{\lambda }}$
$\Rightarrow$ ${\lambda }_p={\displaystyle \frac{hc}{E}}$​
  From de-Broglie’s equation
$\Rightarrow$ ${\lambda }_e={\displaystyle \frac{h}{p}}$
 Since,
$\Rightarrow$ ${\lambda }_p={\lambda }_e$
$\Rightarrow$ ${\displaystyle \frac{hc}{E}}={\displaystyle \frac{h}{p}}$
 $\Rightarrow$ ${\displaystyle \frac{E}{p}}=c$
$=3\times {10}^8$

Therefore, option C is a correct option.

Note:
DE Broglie wavelength plays an important role in physics. It is said that matter incorporates a dual nature of wave-particles. Nuclear physicist waves, named after the discoverer Louis nuclear physicist, is that the property of a fabric object that varies in time or space while behaving the same as waves. It's also called matter-waves. It holds great similarity to the twin nature of sunshine which behaves as particle and wave, which has been proven experimentally.