A nucleus of mass M at rest splits into two parts having masses M′/3 and 2M'/3(M' < M). The ratio of de Broglie wavelength of two parts will be :

Solution

Physics sir · 3 steps

Starting at rest, the two pieces get equal momentum, and λ = h/p does the rest.

1. Momentum conservation. Before the split the total momentum is zero. After it, the two parts must have momenta equal in size and opposite in direction, so p₁ = p₂.

   λ₁/λ₂ = (h/p₁)/(h/p₂) = p₂/p₁ = 1

2. Masses do not matter. The masses M'/3 and 2M'/3 change the speeds, since the lighter part moves twice as fast. But λ depends only on momentum, and the product mv is the same for both.
3. So. The de Broglie wavelengths are equal, and the ratio is 1 : 1, option (c).

The idea to keep. Whenever something at rest breaks into two pieces, the pieces share equal momentum. Equal momentum means equal de Broglie wavelength, whatever their masses.

Answer from the NTA final answer key. Solution by PrepWiser.