20 Nuclear Physics

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 / MeVmass / u
$^2_1H$ deuterium1.11228652.0141018
$^3_1H$ tritrium2.82727373.0160493
$^4_2He$ helium7.07391834.0026032
$^1_0n$ neutron 1.0086649

Method 1: Calculate mass defect $\Delta m$ 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

Thorium as an alternative source of nuclear energy

It’s about time Singapore considered building a liquid fluoride thorium reactor as a safe source of nuclear energy. From the video, it would appear that thorium is safe as it cannot be weaponized, does not require high pressure containers and the risk of a meltdown does not exist. For a small island state like Singapore, this presents an attractive way of obtaining relatively clean abundant energy. I’m sure if we think hard enough we will be able to solve the other problems such as storage of waste products.

Perhaps the part of our syllabus on Nuclear Physics will need to be updated then.