Q. A particle of mass 3m at rest decays into two particles of masses m and 2m having non-zero velocities. The ratio of the de-Broglie wavelengths of the particles (λ_{1}/λ_{2}) is

(a) 1/2

(b) 1/4

(c) 2

(d) none of these

**Ans: (d)**

Sol: Applying Conservation of momentum ,

3mv = mv_{1} + 2mv_{2}

0 = mv_{1} + 2mv_{2}

Hence , v_{1} = − 2v_{2}

Wavelength , $\lambda_1 = \frac{h}{m v_1} $

$\lambda_2 = \frac{h}{2m v_2} = \frac{h}{2m (v_1/2)}$

$\lambda_2 = \frac{h}{m v_1} $

λ_{1}/λ_{2} = 1