1)

The mass of a nucleus  $^{A}_{Z}X$ is less than the sum of the mass 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 m1 and m2 only if (m1+m2) <M . Also two light nuclei of masses m3  and m4 can undergo complete fusion and form a heavy nucleus of mass M ' only if (m3+m4)>M'. The masses of some neutral  atoms are given in the table below:

The kinetic energy (in KeV) of  the alpha particle  . when the nucleus   $^{210}_{84}Po$ at rest undergoes alpha decay, is

A) 5319

B) 5422

C) 5707

D) 5818

Option A

### Explanation:

$_{84}Po^{210}\rightarrow_{2}He^{4}+_{84}Pb^{206}$

Mass defect  $\triangle m=(m_{po}-M_{He}-m_{pb})$ =0.005818 u

$\therefore$    $Q=(\triangle m)(931.48)MeV$

=5.4193 MeV=5419 keV

$\alpha$ ←    →Pb

from conservation of linear  momentum,

ppb= p$\alpha$

$\therefore$   $\sqrt{2m_{pb}k_{pb}}=\sqrt{2m_{\alpha}k_{\alpha}}$

or

$\frac{k_{\alpha}}{k_{pb}}=\frac{m_{pb}}{m_{\alpha}}=\frac{206}{4}$

$\therefore$  $k_{\alpha}=\left(\frac{206}{206+4}\right)(k_{total})$

$=\left(\frac{206}{210}\right)(5419)=5316 keV$