Question

Given below are two statements :

Statement - I : Two photons having equal linear momenta have equal wavelengths.

Statement - II : If the wavelength of a photon is decreased, then its momentum and energy will also decrease.

In the light of the above statements, choose the correct answer from the options given below.

• A. Statement - I is false, but Statement - II is true.
• B. Both Statement - I and Statement - II are true.
• C. Both Statement - I and Statement - II are false.
• D. Statement - I is true, but Statement - II is false.

Answer 1

The correct option is D Statement - I is true, but Statement - II is false.

The energy of a photon is given by :
$E=\frac{hc}{\lambda }$

$\Rightarrow E\propto \frac{1}{\lambda }$

Also, momentum, $p=\frac{\text{E}}{\text{c}}$

$\Rightarrow p\propto E$

$\therefore p\propto E\propto \frac{1}{\lambda }$

$\Rightarrow$ Two photons having equal linear momenta have equal wavelengths.

$\Rightarrow$ If the wavelength of a photon is decreased, then its momentum and energy will increase.

Hence, option $\left(D\right)$ is correct.