(a) Define binding energy in an atom. (b) List three evidence to support the claim that X-rays are electromagnetic waves. (c) List three peaceful uses of nu...

(a) Binding energy

The binding energy of a nucleus is the energy required to completely separate the nucleus into its individual constituent protons and neutrons (equivalently, the energy released when the separate nucleons combine to form the nucleus). It equals the mass defect times \(c^{2}\).

(b) Three evidences that X-rays are electromagnetic waves

• They travel in straight lines with the speed of light and are undeflected by electric or magnetic fields (so they are uncharged).
• They undergo diffraction and interference when passed through crystals.
• They can be polarised.

(c) Three peaceful uses of nuclear energy

• Generation of electricity in nuclear power stations.
• Medical uses: radiotherapy to treat cancer and use of radioisotopes as tracers in diagnosis.
• Industrial and agricultural uses: sterilisation of equipment, food preservation, and thickness/level gauging.

(d) Photoelectric calculation

Data: \(\lambda = 4.5\times10^{-7}\ \text{m}\), work function \(W_{0} = 3.0\times10^{-19}\ \text{J}\) (taking the stated value as \(3.0\times10^{-19}\ \text{J}\)), \(c = 3.0\times10^{8}\ \text{m s}^{-1}\), \(h = 6.6\times10^{-34}\ \text{J s}\).

(i) Frequency: \(f = \dfrac{c}{\lambda} = \dfrac{3.0\times10^{8}}{4.5\times10^{-7}} = 6.67\times10^{14}\ \text{Hz}\).

(ii) Energy of the incident light: \(E = hf = 6.6\times10^{-34}\times6.67\times10^{14} = 4.4\times10^{-19}\ \text{J}\).

(iii) Energy (max KE) of the photoelectrons: \(E_{k} = E - W_{0} = 4.4\times10^{-19} - 3.0\times10^{-19} = 1.4\times10^{-19}\ \text{J}\).