20. Nuclear Physics

existence and size demonstrated using the Rutherford $𝛼$ -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 involve two or more reactants.
represented using the form: $147 𝑁 + 42 𝐻 𝑒 \to 178 𝑂 + 11 𝐻$
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 ( $𝐵 . 𝐸 . 𝐴$ ) 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 $𝐵 . 𝐸 . 𝐴$ versus A graph and why it peaks at $56 𝐹 𝑒$ .

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. $23592 𝑈 + 10 𝑛 \to 23692 𝑈 \to 14456 𝐵 𝑎 + 9036 𝐾 𝑟 + 210 𝑛 + 𝐸 𝑛 𝑒 𝑟 𝑔 𝑦$
nuclear fusion occurs when two light nuclei combine to form a single more massive nucleus, leading to the release of energy.
e.g. $21 𝐻 + 31 𝐻 \to 42 𝐻 𝑒 + 10 𝑛 + 𝐸 𝑛 𝑒 𝑟 𝑔 𝑦$

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

spontaneous and random emission of radiation from a radioactive nucleus.
- $𝛼$ particle – helium nucleus
- $𝛽$ particle – electron
- $𝛾$ particle – electromagnetic radiation

http://youtu.be/Qlb5Z8QBpcI

$𝐴 = - 𝑑 𝑁 𝑑 𝑡 = 𝜆 𝑁$
where A is the rate of disintegration or activity, N is the number of radioactive nuclei and $𝜆$ is the decay constant.
$𝑥 = 𝑥 0 𝑒 - 𝜆 𝑡$
where x could represent the activity, number of undecayed particles or received count rate.
half-life ( $𝑡 12$ ) is the average time taken for half the original number of radioactive nuclei to decay.
From $𝑥 = 𝑥 0 𝑒 - 𝜆 𝑡$ ,
$𝑥 𝑥 0 = 12 = 𝑒 - 𝜆 𝑡 12$
$\Rightarrow - 𝑙 𝑛 2 = - 𝜆 𝑡 12$
$\Rightarrow 𝑡 12 = 𝑙 𝑛 2 𝜆$
You may also use $𝑥 𝑥 0 = 12 𝑡 𝑡 1 / 2$ , as shown in the following video.