JEE Main · 2017 · 02 Apr 2017 · Offline · Modern Physics

A particle A of mass

m

and initial velocity

v

collides with a particle B of mass

\frac{m}{2}

which is at rest. The collision is head on, and elastic. The ratio of the de-Broglie wavelengths

λ_{A}

λ_{B}

after the collision is:

Answer: (D)

Solution

For a head-on elastic collision the standard results give

v_{A}^{'} = \frac{m - \frac{m}{2}}{m + \frac{m}{2}} v = \frac{v}{3}

and

v_{B}^{'} = \frac{2 m}{m + \frac{m}{2}} v = \frac{4 v}{3}

. The de Broglie wavelength is

λ = \frac{h}{p}

, so the ratio is the inverse ratio of momenta:

\frac{λ _{A}}{λ _{B}} = \frac{p _{B}}{p _{A}} = \frac{\frac{m}{2} \cdot \frac{4 v}{3}}{m \cdot \frac{v}{3}} = 2

JEE Main · 2017 · 02 Apr 2017 · Offline · Single correct option