Nuclear (8th and 9th grade)

Modern-day alchemy

Once upon a time, alchemists claimed to be able to turn inexpensive metals into gold.

Modern-day physicists are not able to do so either. However, thanks to our contemporary understanding of the Fundamental interactions, we are able to predict how different substances themselves undergo shapeshifter-like changes to become other substances. The secret agents in this process is the weak interaction. Take a look at the weak interaction!

The result is nuclear radiation, given by atoms that change the properties of their nucleii. The following diagram is a short recap of how the Periodic table of elements works and what atoms can be thought of looking like.

Standard model of particle physics

Physical and mathematical models

Atoms can undergo processes that result in

[[$\alpha$]] radiation, which gives out helium-4 nucleii (which are bundles of two protons and two neutrons)
[[$\beta^-$]] radiation, which gives out an electron and an antineutrino (the antiparticle of a neutrino)
[[$\beta^+$]] radiation, which gives out a positron (antiparticle of an electron) and a neutrino
[[$\gamma$]] radiation, which gives out photons (particles of electromagnetic radiation) of high energy

Fun fact: if a particle (like an electron) meets up with its antiparticle (a positron), both particles get annihilated, resulting in energy
[[$$E = 2mc^2$$]]
In the case of an electron and a positron, the energy released by this annihilation is of around [[$8\cdot 10^{-14}$]]. So, a gram of electrons and positrons being annihilated equals [[$4\cdot 10^{26}$]] joules of instant energy.

The amount of atoms [[$\Delta N$]] undergoing nuclear reactions in a unit of time [[$\Delta t$]] is proportional to the amount [[$N$]] of atoms that have not reacted yet. Mathematically:
[[$$\frac{\Delta N}{\Delta t} = -\lambda N$$]]
for a constant [[$\lambda$]].