Paragraph: The mass of a nucleus ${ }_{Z}^{A} X$ is less than the sum of the masses of $(A-Z)$ number of…

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 $\left(m_{1}+m_{2}\right) < M$. 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 $\left(m_{3}+m_{4}\right) > M^{\prime}$. The masses of some neutral atoms are given in the table below:
$\left(1 u=932 M e V / c^{2}\right)$
Question: The correct statement is
  1. The nucelus 3 6 Li can emit an alpha particle.
  2. The nucleus 84 210 Po can emit a proton.
  3. Deuteron and alpha particle can undergo complete fusion.
  4. The nuclei 30 70 Zn and 34 82 Se can undergo complete fusion.

Solution

(A)   3 Li 7 2 He 4 + 1 H 3
Δ m = M Li - M He - M H 3
= 6.01513 - 4.002603 - 3.016050
= - 1.003523 u
Δ m  is negative so reaction n is not possible.
(B)   84 Po 210 83 Bi 209 + 1 P 1
Δ m  is negative so reaction is not possible.
(C)   1 H 2 2 He 4 + 3 Li 6
Δ m  is positive so reaction is possible.
(D)   30 Zn 70 + 34 Se 82 64 Gd 152
Δ m  is positive so reaction is not possible.

Asked in: JEE Advanced 2013 (Paper 2)

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