Question

Two photons having

• A. Equal wavelengths have equal linear momentum
• B. Equal energies have equal linear momentum
• C. Equal frequencies have equal linear momentum
• D. Equal linear momentum have equal wavelengths

Answer 1

The correct option is D

Equal linear momentum have equal wavelengths

Option a says if ${\lambda }_1={\lambda }_2$

Then $P_1=P_2$

Well we know P = $\frac{h}{\lambda }$

Where h is plank's constant.

So if wavelength is the same then momentum of photons will also be the same.

Is that all ?

No
if wavelength is the same then magnitude of momentum will be the same, but not necessarily the same direction.

Wavelength is a scalar quantity.

Momentum is a vector quantity, so this statement is not true.

Option b says if $E_1=E_2$ then $P_1=P_2$

Well we know P =$\frac{E}{c}$ where c is speed of light in vacuum which is constant. So if E is same then momentum will be same.

Only the magnitude . Energy is a scalar. The P in the equation refers to the magnitude.

So even option b is not entirely true.

Option c is if FREQUENCY IS EQUAL

${Ѵ}_1={Ѵ}_2$ then $P_1=P_2$

Again if frequency is equal then wavelength will be equal as speed is anyway going to be 'c' , a constant. (c=$\lambda$Ѵ)

So same argument as for option A

Option d is if

${\overrightarrow{p}}_1={\overrightarrow{p}}_2$ then ${\lambda }_1={\lambda }_2$

here ${\overrightarrow{p}}_1$&${\overrightarrow{p}}_2$ vectors are same.(same direction and magnitude)

$\Rightarrow \frac{h}{{\lambda }_1}=\frac{h}{{\lambda }_2}\Rightarrow {\lambda }_1={\lambda }_2$