# Question is based on the following paragraph.A nucleus of mass $\dpi{100} M\; +\; \Delta m\;$ is at rest and decays into two daughter nuclei of equal mass $\dpi{100} \frac{M}{2}$ each. Speed of light is $\dpi{100} c$ .Question: The binding energy per nucleon for the parent nucleus is $\dpi{100} E_{1}$ and that for the daughter nuclei is $\dpi{100} E_{2}$ .Then Option 1) $E_{1}=2E_{2}\; \;$ Option 2) $\; E_{2}=2E_{1}\;$ Option 3) $\; \;E_{1}> E_{2}\;$ Option 4) $\; \; E_{2}>E_{1}$

As we learnt in

Binding energy per nucleon -

- wherein

This graph shows the stability of nuclei many nuclear phenomena can be explained by this graph

Product must be more stable than the original nucleus.

Hence, Binding energy of product > Binding energy of reactant.

$\therefore\ \; E_{2}>E_{1}$

Correct option is 4.

Option 1)

$E_{1}=2E_{2}\; \;$

This is an incorrect option.

Option 2)

$\; E_{2}=2E_{1}\;$

This is an incorrect option.

Option 3)

$\; \;E_{1}> E_{2}\;$

This is an incorrect option.

Option 4)

$\; \; E_{2}>E_{1}$

This is the correct option.

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