2 Size of Nucleus

Size of Nucleus

• It was found experimentally that the volume of a nucleus is proportional to its mass number (A).
• Let

R → Radius of the nucleus

∴Volume

Where, R₀ is a constant = 1.2 × 10⁻¹⁵ m is the range of nuclear force

• The density of nuclei of all the atoms is same as it is independent of mass number.
• Mass is another form of energy. One can convert mass-energy into other form of energy.
• Mass-energy equivalence relation is E = mc²

Where,

m → Mass

c → Speed of light

Nuclear Binding Energy

• The difference in mass of a nucleus and its constituents is called the mass defect.
• Binding energy of a nucleus is the energy with which nucleons are bound in the nucleus.

Expression for Binding Energy

• In a nucleus ,

Z = Number of protons

A = Number of protons + Number of neutrons

Let m_p = Mass of a proton

m_n = Mass of a neutron

m_N = Mass of nucleus

∴Mass defect,

Δm = [Zm_p + (A − Z) m_n − m_N]

• Using Einstein’s mass-energy equivalence,

Binding energy = ΔmC²

• Average binding energy per nucleon is given by the total binding energy divided by the mass number of the nucleus.

• Binding energy per nucleon is practically constant for mass number. (30 < A < 170)
• Binding energy per nucleon is lower for both light nuclei (A < 30) and heavy nuclei (A > 170).

Importance of Binding energy curve

• As we move from heavy nuclei region to the middle region of the plot, there is a gain in the overall binding energy and hence, in the release of energy. This indicates that energy can be released when a heavy nucleus breaks into roughly two equal fragments.

This process is called nuclear fission.

• When we move from lighter nuclei to heavier nuclei, there will be gain in the overall binding energy and release of energy. This is called nuclear fusion.