Question

A particle of mass 3m at rest decays into two particles of masses m and 2m having non-zero velocities. The ratio of the de Broglie wavelengths of the particles $\left({\lambda }_1/{\lambda }_2\right)$ is

• A. 1/2
• B. 1/4
• C. 2
• D. None of these

Answer 1

The correct option is A 1/2

By conservation momentum, $3mv=m{v}_1+2m{v}_2$

At mass 3m is at rest so $v=0$

Now, $0=m{v}_1+2m{v}_2$ or $p_1+2p_2=0$ where $p_1,p_2$ are the momentum of m and 2m.

Thus, $|p_1|=2|p_2|...\left(1\right)$

So, ${\lambda }_1=\frac{h}{|p_1|}$ and ${\lambda }_2=\frac{h}{|p_2|}$

Thus, $\frac{{\lambda }_1}{{\lambda }_2}=\frac{|p_2|}{|p_1|}=1/2$ using (1)