# 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.
• $x=x_0{e^{-\lambda t}}$
• 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.