Question

A particle of mass $8~\mu g$ collides with another stationary particle of mass $4~\mu g$. If the collision is perfectly elastic and one dimensional, the ratio of de Broglie wavelengths after collision is

• A. $4:1$
• B. $3:1$
• C. $1:1$
• D. $2:1$

Hint:

Use de Broglie formula and post-collision velocities from elastic collision formulas.

Answer 1

The Correct Option is D

Perfect elastic collision, one dimensional
Using conservation of momentum and energy
Final velocity of $8~\mu g$ particle: $v_1' = \dfrac{m_1 - m_2}{m_1 + m_2}v$
Final velocity of $4~\mu g$ particle: $v_2' = \dfrac{2m_1}{m_1 + m_2}v$
de Broglie wavelength $\lambda = \dfrac{h}{mv}$
So $\lambda_1 : \lambda_2 = \dfrac{1}{m_1 v_1'} : \dfrac{1}{m_2 v_2'} = \dfrac{1}{8 \cdot v_1'} : \dfrac{1}{4 \cdot v_2'} = 2:1$