Q 12-11-152JEE MainJEE Main 2020 (4 Sep, Shift 1)Medium
Particle $A$ of mass $m_A = \dfrac m2$ moving along the $x$-axis with velocity $v_0$ collides elastically with another particle $B$ at rest having mass $m_B = \dfrac m3$. If both the particles move along the $x$-axis after the collision, the change $\Delta\lambda$ in the wavelength of the particle $A$, in terms of its de-Broglie wavelength $(\lambda_0)$ before the collision is:
Answer: (D) $\Delta\lambda = 4\lambda_0$
For a 1-D elastic collision with $B$ at rest:
$$v_A = \frac{m_A - m_B}{m_A + m_B}v_0 = \frac{1/2 - 1/3}{1/2 + 1/3}v_0 = \frac{v_0}{5}$$
$\lambda \propto \dfrac1v$, so the new wavelength is $5\lambda_0$ and $\Delta\lambda = 4\lambda_0$.
Solution by Sreeraj P, M.Sc Physics