First slide

Matter waves (DC Broglie waves)

Question

A particle of mass M at rest decays into two particles of masses $m_{1} and m_{2}$ having non-zero velocities. The ratio of the de-Broglie wavelengths of the particles $λ_{1} / λ_{2}$ is

Easy

A

$m_{1} / m_{2}$
B

$m_{2} / m_{1}$
C

1.0
D

$\sqrt{m_{2}} / \sqrt{m_{1}}$

Solution

By law of conservation of momentum
$0 = m_{1} \vec{v_{1}} + m_{2} \vec{v_{2}} \Rightarrow m_{1} \vec{v_{1}} = - m_{2} \vec{v_{2}}$
- ve sign indicates that both the particles are moving in opposite direction. Now de-Broglie wavelengths
$\begin{array}{l} λ_{1} = \frac{h}{m_{1} v_{1}} and λ_{2} = \frac{h}{m_{2} v_{2}}; \\ ∴ \frac{λ_{1}}{λ_{2}} = \frac{m_{2} v_{2}}{m_{1} v_{1}} = 1 \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App