# 20. Nuclear Physics

### The Nucleus

• existence and size demonstrated using the Rutherford $$\alpha$$-scattering experiment.
• consists of nucleons (protons and neutrons)
• isotopes of an element share the same number of protons but different number of neutrons.

### Nuclear Reactions

• nuclear reactions involve two or more reactants.
• represented using the form: $${^{14}_7N}+{^4_2He}\rightarrow{^{17}_8O}+{^1_1H}$$
• for a reaction that releases energy, mass-energy of reactants = mass-energy of products + E,
where $$E = mc^2$$ and m is the mass defect (difference in mass between the products and reactants).
• binding energy is the energy released when the nucleus is formed from its separate protons and neutrons. The same amount of energy is required to break up a nucleus into its constituent nucleons.

• binding energy per nucleon ($$\frac{B.E.}{A}$$) is an indication of the stability of a nucleus, where B.E .is binding energy and A is the nucleon number. You need to know how to sketch its variation with nucleon number. (The following video explains the shape of the $$\frac{B.E.}{A}$$ versus A graph and why it peaks at $$^{56}Fe$$.

• nuclear fission is the disintegration of a heavy nucleus into two lighter nuclei of comparable mass with the emission of neutrons and release of energy.
e.g. $${^{235}_{92}U}+{^1_0n}\rightarrow{^{236}_{92}U}\rightarrow{^{144}_{56}Ba}+{^{90}_{36}Kr}+2^1_0n+Energy$$
• nuclear fusion occurs when two light nuclei combine to form a single more massive nucleus, leading to the release of energy.
e.g. $${^2_1H}+{^3_1H}\rightarrow{^4_2He}+{^1_0n}+Energy$$

• The following quantities are always conserved:
• proton number & neutron number
• momentum
• mass-energy

• $$\alpha$$ particle – helium nucleus
• $$\beta$$ particle – electron
• $$\gamma$$ particle – electromagnetic radiation

• $$A=-\frac{dN}{dt}=\lambda N$$
where A is the rate of disintegration or activity, N is the number of radioactive nuclei and $$\lambda$$ is the decay constant.
• $$x=x_0{e^{-\lambda t}}$$
where x could represent the activity, number of undecayed particles or received count rate.
• half-life ($$t_{\frac{1}{2}}$$) is the average time taken for half the original number of radioactive nuclei to decay.
• From $$x=x_0{e^{-\lambda t}}$$,
$$\frac{x}{x_0}=\frac{1}{2}=e^{-\lambda t_{\frac{1}{2}}}$$
$$\Rightarrow{-ln2}=-\lambda t_{\frac{1}{2}}$$
$$\Rightarrow{t_{\frac{1}{2}}}=\frac{ln 2}{\lambda}$$
• You may also use $${\frac{x}{x_0}}={\frac{1}{2}}^{\frac{t}{t_{1/2}}}$$, as shown in the following video.