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, 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

The correct option is C $3.00\times {10}^8$

Given:-

Wavelength of photon & electron are equal

$\Rightarrow {\lambda }_p={\lambda }_e={10}^{-9}m$

$E$=Energy of photon

$P$= Momentum of electron

Solution:-

From Planck's equation

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

From de-broglie's equation

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

Since ${\lambda }_p={\lambda }_e\Rightarrow \frac{hc}{E}=\frac{h}{p}$

$\Rightarrow \frac{E}{p}=C=3\times {10}^8$