Question

Assume a hypothetical nuclear fission reaction:
$X\to Y+Z$
If the atomic masses of $X,Y\&Z$ are respectively $x,y\&z$ calculate the maximum amount of heat generated if 1 gram of X undergoes fission. Consider the molar mass of X to be M.

• A. $\frac{N_A}{M}\times (y-z-x)c^{2}units$
• B. $\frac{N_A}{M}\times (x-y-z)c^{2}units$
• C. $\frac{N_A}{M}\times (x-y+z)c^{2}units$
• D. $M\times (x-y-z)c^{2}units$

Answer 1

The correct option is B $\frac{N_A}{M}\times (x-y-z)c^{2}units$

We discussed that there is a release of energy in the nuclear fission reaction. Connect the dots using the following algorithm.
Calculate the rest mass energy of the parent
Calculate the total rest mass energy of the daughters(This will obviously be less than the value calculated in the first step
Subtract them, this is the energy that released
This energy first is taken by the daughters in form of their energy
They are suddenly stopped in the bulk and all this kinetic energy is converted to heat
You have now heat generated in one fission reaction, calculate in 1 gram of X how many nuclei will be present.
Calculate thus the total heat.
So, let's begin.
Energy released=Rest mass energy of parent nucleus - total rest mass energy of the daughter nuclei.
$(x-y-z)c^2$.
Also, since the molar mass is M, in M group of X we have $N_A$ no, of X nuclei.
Hence in 1 gram we will have $\frac{N_A}{M}$ nuclei.
Now, 1 nucleus releases $(x-y-z)c^2$ amount of energy.
So, $\frac{N_A}{M}$ nuclei will release,
$\frac{N_A}{M}\times (x-y-z)c^2$ units of energy.