# 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 (λ1/λ2) is

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 (λ12) is

(a) 1/2

(b) 1/4

(c) 2

(d) none of these

Ans: (d)

Sol: Applying Conservation of momentum ,

3mv = mv1 + 2mv2

0 = mv1 + 2mv2

Hence , v1 = − 2v2

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

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

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

λ12 = 1