Question

Binding energy per nucleon versus mass number curve for nuclei is shown in the figure. $\text{W, X, Y}$ and $\text{Z}$ are four nuclei indicated on the curve. The process that would release energy is

• A. $Y\to 2Z$
• B. $W\to X+Z$
• C. $X\to Y+Z$
• D. $W\to 2Y$

Answer 1

The correct option is D $W\to 2Y$

Energy is released in a process when total binding energy $(\text{B.E.)}$ of products is more than that of the reactants.

For option $\left(\text{A}\right)$:

$\text{Y}\to 2\text{Z}$

$B.E.$ of reactants

$B_R=60\times 8.5\text{MeV}=510\text{MeV}$

$B.E$ of products

$B.E_P=2\times (30\times 5\text{MeV})=300\text{MeV}$

$\Rightarrow B.E_P<B.E_R$

For option $\left(B\right)$:

$W\to X+Z$

$B.E_R=120\times 7.5\text{MeV}=900\text{MeV}$

$B.E_P=(90\times 8)+(30\times 5)=870\text{MeV}$

$\Rightarrow B.E_P<B.E_R$

For option $\left(C\right)$:

$X\to Y+Z$

$B.E_R=90\times 8\text{MeV}=720\text{MeV}$

$B.E_P=(60\times 8.5)+(30\times 5)=660\text{MeV}$

$\Rightarrow B.E_P<B.E_R$

For option $\left(D\right)$:

$W\to 2Y$

$B.E_R=120\times 7.5\text{MeV}=900\text{MeV}$

$B.E_P=2\times (60\times 8.5\text{MeV})=1020\text{MeV}$

$\Rightarrow B.E_P>B.E_R$

Hence, option $\left(D\right)$ is correct.