Calculating Energy Change in Nuclear Reactions

There are two methods of calculating the energy released in a nuclear reaction, which will be demonstrated using an example. Consider the nuclear reaction:

$$^2_1H + ^3_1H \rightarrow ^4_2He + ^1_0n$$

The table below shows the values of mass and binding energy per nucleon.

	binding energy per nucleon / MeV	mass / u
$^2_1H$ deuterium	1.1122865	2.0141018
$^3_1H$ tritrium	2.8272737	3.0160493
$^4_2He$ helium	7.0739183	4.0026032
$^1_0n$ neutron		1.0086649

Method 1: Calculate difference in mass $\Delta m$ and take $E = \Delta m c^2$

$\Delta m$ = 2.0141018 + 3.0160493 – 4.0026032 – 1.0086649 = 0.0188830 u

$E = \Delta m c^2$
= 0.0188830 × 1.66054 × 10^-27 kg × (2.99792 × 10⁸ m s^-1)²
= 2.8181 × 10¹² J
= 17.589 MeV

Method 2: Calculate difference in binding energy

Changing in B.E. = B.E. of $^4_2He$ – (B.E. of $^2_1H$ + B.E. of $^3_1H$)
= 4(7.0739183) MeV – [2(1.1122865) + 3(2.8272737)] MeV
= 17.589 MeV