Question

A particle of mass M at rest decays into two particles of masses $m_1$ and $m_2$, having non-zero velocities. The ration of the de-Broglie wavelengths of the particles, $I_1$/$I_1$ is

• A. $m_1$/$m_2$
• B. $m_2$/$m_1$
• C. 1
• D. ${\omega }_2/{\omega }_1$

Answer 1

Answer: (B)

$m_2$/$m_1$

$\begin{array}{cc}\lambda & =\frac{h}{\sqrt{2m{k}_e}}=\frac{h}{\sqrt{2m\times \frac{1}{2}m{v}^2}}\\ \therefore \lambda \propto \frac{1}{\sqrt{m_2}}& \Rightarrow \lambda \propto \frac{1}{m}\\ [& \therefore \frac{{\lambda }_1}{{\lambda }_2}=\frac{m_2}{m_1}]\\ \therefore & \text{option}B\text{is}\end{array}$