Question

When a U²³⁸ nucleus originally at rest, decays by emitting an alpha particle having a speed 1.5 × 10⁷ ms^-1. Then, calculate the kinetic energy of the residual nucleus.

Answer 1

₉₂U²³⁸ → ₉₀Th²³⁴ + ₂He⁴ (α-particle)
If mass of one nucleon is m, then according to principle conservation of momentum, Momentum of residual = Momentum of α-particle nucleus

∵ The mass of one nucleon m = 1.67 x 10^-27 kg
∴ Mass of Thorium nucleus
\(m_{t h}=234 \times 1.67 \times 10^{-27} \mathrm{kg}\)
∴ Kinetic energy of esidual nucleus,