The mass of nucleus `._(z)X^(A)` 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 mass `m_(1)` and `m_(2)` only if `(m_(1)+m_(2)) lt M`. Also two light nuclei of massws `m_(3)` and `m_(4)` can undergo complete fusion and form a heavy nucleus of mass `M` ''only if `(m_(3)+m_(4)) gt M`''. The masses of some neutral atoms are given in the table below.
`|{:(._(1)^(1)H,1.007825u,._(1)^(2)H,2.014102u,),(._(1)^(3)H,3.016050u,._(2)^(4)H,4.002603u,),(._(3)^(6)Li,6.015123u,._(3)^(7)Li,7.016004u,),(._(30)^(70)Zn,69.925325u,._(34)^(82)Se,81.916709u,),(._(64)^(152)Gd,151.91980u,._(82)^(206)Pb,205.97445u,),(._(83)^(209)Bi,208.980388u,._(84)^(210)Po,209.982876u,):}|`
The kinetic energy ( in `KeV`) of the alpha particle, when the nucleus at rest undergo alpha decay, is

Options

A. `5319`
B. `5422`
C. `5707`
D. `5818`

Answer

A

Explanation

`._(84)^(210)Po rarr_(2)^(4)He+_(82)^(206)Pb`
`Q=(209.982876-4.002603-205.97455)C^(2)`
`=5.422 MeV`
From conservation of momentum.
`:. K_(1)=5.319 MeV=5319 KeV`