All Problems

Radioactivity

Problem 6.234

A stationary \(\mathrm{Pb}^{200}\) nucleus emits an alpha-particle with kinetic energy \(T_{\alpha}=5.77 \mathrm{MeV}\). Find the recoil velocity of a daughter nucleus. What fraction of the total energy liberated in this decay is accounted for by the recoil energy of the daughter nucleus?

Reveal Answer
v=2mαTα/m=3.4105 m/s;0.020v=\sqrt{2 m_{\alpha} T_{\alpha} / m}=3.4 \cdot 10^{5} \mathrm{~m} / \mathrm{s} ; 0.020