Q: The kinetic energy of α – particles emitted in the dacay of _{88} Ra^{226} into _{86} Ra^{222} 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.