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Paragraph: The mass of a nucleus \({ }_{Z}^{A} X\) is less than the...

Paragraph:

The mass of a nucleus \({ }_{Z}^{A} X\) is less than the sum of the masses of \((A-Z)\) number of neutrons and \(Z\) number of protons in the nucleus. The energy equivalent to the corresponding mass difference is known as the binding energy of the nucleus. A heavy nucleus of mass \(M\) can break into two light nuclei of masses \(m_{1}\) and \(m_{2}\) only if \(\left(m_{1}+m_{2}\right) \lt M\). Also two light nuclei of masses \(m_{3}\) and \(m_{4}\) can undergo complete fusion and form a heavy nucleus of mass \(M^{\prime}\) only if \(\left(m_{3}+m_{4}\right) \gt M^{\prime}\). The masses of some neutral atoms are given in the table below:




\(\left(1 u=932 M e V / c^{2}\right)\)


Question:

The kinetic energy (in \(k e V\) ) of the alpha particle, when the nucleus \({ }_{84}^{210} P o\) at rest undergoes alpha decay, is
5320
5422
5707
5818
Solution:
84 Po 210 + 2 He 4 82 Pb 206
Δ m = M PO - M He - M Pb = 0.008421 u
Q = 0.008421 × 9 3 2  MeV = 5 4 2 2  KeV
K α = 2 1 0 2 1 4 × 5 4 2 2  KeV = 5 3 2 0  KeV