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:

21⁢𝐻+31𝐻→42𝐻⁡𝑒+10𝑛

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

	binding energy per nucleon / MeV	mass / u
21⁢𝐻 deuterium	1.1122865	2.0141018
31⁢𝐻 tritrium	2.8272737	3.0160493
42⁢𝐻⁡𝑒 helium	7.0739183	4.0026032
10⁢𝑛 neutron		1.0086649

Method 1: Calculate difference in mass Δ⁢𝑚 and take 𝐸 =Δ⁢𝑚⁢𝑐2

Δ⁢𝑚 = 2.0141018 + 3.0160493 – 4.0026032 – 1.0086649 = 0.0188830 u

𝐸 =Δ⁢𝑚⁢𝑐2
= 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 42⁢𝐻⁡𝑒 – (B.E. of 21⁢𝐻 + B.E. of 31⁢𝐻)
= 4(7.0739183) MeV – [2(1.1122865) + 3(2.8272737)] MeV
= 17.589 MeV