Q: The kinetic energy of α – particles emitted in the dacay of 88 Ra226 into 86 Ra222 is measured to be 4.78 MeV. What is the total disintegration energy or the ‘Q – value of this process’?
Sol: The standard relation between the kinetic energy of the - particle (KE_) and the Q-value (or total
disintegration energy) is
$\large K.E_{\alpha} = \frac{A-4}{A}.Q $
$\large Q = \frac{A}{A-4}.K.E_{\alpha} $
$\large Q = \frac{226}{226-4}\times 4.78 MeV $
Q = 4.865 MeV ≈ 4.87 MeV.