Question

A heavy nucleus at rest breaks into two fragments which fly off with velocities in the ratio $8:1$. the ratio of de-broglie wavelengths of fragments are

• A. $1:2$
• B. $1:8$
• C. $4:1$
• D. None of these

Answer 1

The correct option is A $1:2$

Momentum conversation. Given,

$m_1{V}_1=m_2{V}_2$

$\frac{V_1}{V_2}=\frac{8}{1}=\frac{m_2}{m_1}$

So, $\frac{m_1}{m_2}=\frac{1}{8}$

but when particle break then density $=$ constant

So, $V\alpha m$

$\frac{V_1}{V_2}=\frac{m_1}{m_2}$

$\frac{a_1^3}{a_2^3}=\frac{1}{8}$

$\frac{a_1}{a_2}={\left(\frac{1}{8}\right)}^{1/3}\Rightarrow \frac{a_1}{a_2}=\frac{1}{2}$

$\Rightarrow a_1:a_2=1:2$