Nuclear Energy

The protons and neutrons in the nucleus of an atom are called nucleons. The energy required to completely separate the protons and the neutrons of an atom is called binding energy. It’s also the energy that would be released if individual protons and neutrons were combined into a single nucleus.

Binding energy is the energy released to join or fuse together the nucleons of the nucleus.

When the nucleus of an atom is separated, the combined mass of protons and neutrons when added together is greater than the mass of the nucleus as a unit

The difference in mass is called Mass Defect. Mass defect is the gain or loss in mass, produced when the protons and neutrons in the nucleus are separated or joined together. 

Mass defect = sum of masses of proton and neutron – mass of nucleus 

• Δm = mass defect 

Einstein showed that mass and energy are related by the equation:

E = mc²

E = Δmc² 

• E = energy released 
• Δm = is the mass defect 
• c = speed or velocity of light 

Electron volt is the energy possessed by an electron that is moving under the influence of a potential difference of one volt. It is the unit of energy in nuclear energy.

Value of electron volt (eV):

• 1 eV = 1.6 × 10^-19 J
• 1 MeV = 1.602 × 10^-13 J

Atomic mass unit ( a.m.u.):

The unit of energy is also expressed in a.m.u.

1 amu = 1.66 × 10^-27 Kg = 931 Mev = 1.49 × 10^-10 J

Example 9.4.1:

In a nuclear fission process, the mass defect was 2.4 × 10^-5 kg. Calculate the energy released. [speed of the light in vacuumA vacuum is an area of space containing little or no matter (solids, liquids, and gases). It is a space with nothing in it, not even air. More = c = 3.0 × 10⁸ ms^-1]

Solution

Recall that,

E = mc²

E = 2.4 × 10^-5 × (3 × 10⁸)²

E = 2.4 × 10^-5 × 9 × 10¹⁶

E = 2.16 × 10¹² J

Example 9.4.2:

a. Calculate the energy of 2.25 eV
b. What is the value of 2.5 JoulesJoule is the SI (International System of Units) unit of energy and work. It is equal to the amount of work done when a force of 1 newton displaces a mass... More in a.m.u?

Solution

a. 1 eV = 1.6 × 10^-19 J

Therefore,

2.25 eV will equal 2.25 × 1.6 × 10^-19

= 3.6 × 10^-19 Joules

b. 1 amu = 931 Mev = 1.49 × 10^-10 J

x amu = \( \frac{2.5}{1.49 \: \times \: 10^{-10}} \scriptsize \: \times \: 1 \)

= 1.67 × 10¹⁰ amu