Question

A particle of mass M at rest decays into particles of masses $m_{1}and{m}_2$ having non -zero velocities. The ratio of the de broglie wavelengths of the particles ${\lambda }_1/{\lambda }_2$ is :

• A. $m_1/m_2$
• B. $m_2/m_1$
• C. 1
• D. m1.m2

Answer 1

The correct option is C 1

When mass M at rest (initial momentum = 0) decays to smaller masses $m_1\&m_2$ they have same momentum (from conservation of momentum)

$\overrightarrow{P_1}+\overrightarrow{P_2}=0$

$\Rightarrow P_1=P_2$ (in magnitude)

And de-Broglie wavelength,

${\lambda }_1=\frac{h}{P_1}{\lambda }_2=\frac{h}{P_2}$ [h : planck, constant]

thus we get,

${\lambda }_1={\lambda }_2$ (Req $\alpha$) $\Rightarrow \frac{{\lambda }_1}{{\lambda }_2}=1$