20. Nuclear Physics

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

Radioactive Decay

  • spontaneous and random emission of radiation from a radioactive nucleus.
    • \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.