Question

Use the graph of binding energy to estimate the total energy released if a nucleus with mass number 240 fissions into two nuclei with mass number 120.

Short answer

The amount of energy released in the nuclear reaction involves when a nucleus of mass number 240 decays into two nucleus of each has mass number 120 approximately is $168\text{MeV}$.

Step-by-step solution

Step.1.

The plot binding energy per nucleon verses mass number is given as the figure 42.6 in the text book. In this plot, the corresponding binding energy per nucleon for mass number 240 approximately is $7.8\text{MeV}$. The corresponding binding energy per nucleon for mass number 120 approximately is $8.5\text{MeV}$.

The total binding energy of nucleus of mass number 240 is,

$\begin{array}{l}{E}_1=240\left(7.8\text{MeV}\right)\\ =1872\text{MeV}\end{array}$

The total binding energy of two nuclei of each of mass number 120 is,

$\begin{array}{l}{E}_2=120\left(8.5\text{MeV}\right)+120\left(8.5\text{MeV}\right)\\ =2040\text{MeV}\end{array}$

Step.2

The amount of energy released in the nuclear reaction involves when a nucleus of mass number 240 decays into two nucleus of each has mass number 120 is,

$\begin{array}{l}\Delta E=E_2-E_1\\ =2040\text{MeV}-1872\text{MeV}\\ =168\text{MeV}\end{array}$

Therefore, the amount of energy released in the nuclear reaction involves when a nucleus of mass number 240 decays into two nucleus of each has mass number 120 approximately is$168\text{MeV}$.