Question

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

• A. $m_1:m_2$
• B. $m_2:m_1$
• C. $1:1$
• D. $\sqrt{m_2}:\sqrt{m_1}$

Answer 1

The correct option is C $1:1$

Let $v_1,v_2$ be velocities of $m_1,m_2$

Using Conservation of momentum,
$P_i=P_f$
$0=m_1{v}_1-m_2{v}_2$
$\Rightarrow m_1{v}_1=m_2{v}_2$

De-Broglie wavelengths of the particles are

${\lambda }_1=\frac{h}{m_1{v}_1}$
${\lambda }_2=\frac{h}{m_2{v}_2}$
$\Rightarrow \frac{{\lambda }_1}{{\lambda }_2}=1$