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: $${}_7^{14}N+{}_2^{4}He\to {}_8^{17}O+{}_1^{1}H$$
• for a reaction that releases energy, mass-energy of reactants = mass-energy of products + E,
  where $$E=m{c}^2$$ 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. $${}_{92}^{235}U+{}_0^{1}n\to {}_{92}^{236}U\to {}_{56}^{144}Ba+{}_{36}^{90}Kr+2_0^{1}n+Energy$$
• nuclear fusion occurs when two light nuclei combine to form a single more massive nucleus, leading to the release of energy.
  e.g. $${}_1^{2}H+{}_1^{3}H\to {}_2^{4}He+{}_0^{1}n+Energy$$

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

Radioactive Decay

• spontaneous and random emission of radiation from a radioactive nucleus.
  • $$\alpha$$ particle – helium nucleus
  • $$\beta$$ particle – electron
  • $$\gamma$$ particle – electromagnetic radiation

http://youtu.be/Qlb5Z8QBpcI

• $$A=-\frac{dN}{dt}=\lambda N$$
  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 $$x=x_0{e}^{-\lambda t}$$,
  $$\frac{x}{x_0}=\frac{1}{2}=e^{-\lambda t_{\frac{1}{2}}}$$
  $$\Rightarrow -ln2=-\lambda t_{\frac{1}{2}}$$
  $$\Rightarrow t_{\frac{1}{2}}=\frac{ln2}{\lambda }$$
• You may also use $$\frac{x}{x_0}={\frac{1}{2}}^{\frac{t}{t_{1/2}}}$$, as shown in the following video.