Question

A nucleus of mass M initiallyat rest splits into 2 fragments of masses M^"/3 and 2M^'/3 ( M< M^'). Find the ratio of de brofliewavelengths of the two fragments.

Answer 1

$$\begin{gathered} de-brogliewavelength: \\ \lambda =\frac{h}{mv} \\ \frac{{\lambda }_1}{{\lambda }_2}=\frac{m_2}{m_1}\times \frac{v_2}{v_1} \\ Fromlawofconservationofmomentum, \\ \frac{M}{3}{v}_1=\frac{2M}{3}{v}_2 \\ \frac{v_1}{v_2}=\frac{2}{1} \\ Hence, \\ \frac{{\lambda }_1}{{\lambda }_2}=\frac{\frac{2M}{3}}{\frac{M}{3}}\times \frac{1}{2} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{1}\mathbf{:}\mathbf{1} \end{gathered}$$