Question

A particle of mass $M$ , at rest decays into two masses $m_1$ and $m_2$ with non-zero velocities. The ratio of de Broglie wavelengths of the particles $\frac{{\lambda }_1}{{\lambda }_2}$ is $\frac{m}{n}$ , then the minimum value of $m+n$ is

• A. 3
• B. 4
• C. 2
• D. 5

Answer 1

Answer: (C)

As there is no external force
Linear momentum will be conserved
${\text{P}}_1={\text{P}}_2=\text{P}$
Now, de-Broglie wavelength
${\lambda }_1=\frac{h}{P_1}\text{ or }{\lambda }_2=\frac{h}{P_2}$
$\Rightarrow$ $\frac{{\lambda }_1}{{\lambda }_2}=\frac{{\text{P}}_2}{{\text{P}}_1}=\frac{\text{P}}{\text{P}}=1$ $=\frac{m}{n}$
$\Rightarrow m+n=1+1=2$