Question

A particle of mass $M$ at rest decays into two particles of mass $m_1$ and $m_2$, having non-zero velocities. The ratio of the de-Broglie wavelength of the particles, ${\lambda }_1/{\lambda }_2$ is:

• A. $m_1/m_2$
• B. $m_2/m_1$
• C. $1.0$
• D. none of these

Answer 1

The correct option is C $1.0$

answer is option c

$m_1{m}_2$

$v_1{v}_2$

Conservation of momentum

$0=m_1{v}_1+m_2{v}_2$

$\Rightarrow m_1{v}_1=-m_2{v}_2$

$\Rightarrow \frac{v_1}{v_2}=\frac{m_2}{m_1}$

De Broglies wave equation is

$\lambda =\frac{h}{p}=\frac{h}{mv}$

so the ratio $=\frac{{\lambda }_1}{{\lambda }_2}=\frac{\frac{h}{m_1{v}_1}}{\frac{h}{m_2{v}_2}}$

$=\frac{m_2{v}_2}{m_1{v}_1}$

$\frac{m_2}{m_1}\times \frac{v_2}{v_1}$

$\frac{m_2}{m_1}\times \frac{m_1}{m_2}=1$