In a nuclear fission reaction of an isotope of mass M, three similar daughter nuclei of same mass are formed. The speed of a daughter nuclei in terms of mass defect Δ M will be :

Solution

Physics sir · 4 steps

Mass defect energy becomes the total kinetic energy of three equal pieces moving at one common speed.

1. Energy released. The mass defect turns into energy Δ M c². This energy appears as the kinetic energy of the daughter nuclei.
2. Equal speeds. Each daughter has mass about M/3, since Δ M is tiny compared with M. The parent was at rest, so total momentum is zero. The usual assumption is that the energy is shared equally, so each daughter moves with the same speed v, 120° apart, which keeps the total momentum zero.

   3 × 1/2(M/3)v² = Δ M c²

3. Solve for v. The left side is 1/2Mv², so v² = (2Δ M c²)/M.
4. So. v = c√((2Δ M)/M), which is option (c).

The idea to keep. In fission or decay from rest, set the mass defect energy Δ M c² equal to the total kinetic energy of the products. Momentum conservation tells you how the speeds are shared.

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