Explain atomic energy levels and spectra, the Standard Model, mass-energy equivalence and nuclear reactions

What this dot point is asking

WACE wants you to link three ideas: that quantised atomic energy levels explain spectral lines, that the Standard Model classifies fundamental particles, and that mass-energy equivalence accounts for the energy released in nuclear reactions through mass defect and binding energy. The recurring tool is energy conservation, now allowing mass to count as energy.

Atomic energy levels and spectra

Electrons in an atom can only occupy discrete energy levels. An electron drops from a higher level $E_i$ to a lower level $E_f$ by emitting a single photon whose energy equals the gap,

Because only certain gaps exist, only certain photon energies (and so certain wavelengths) appear: an emission spectrum is a set of bright lines on a dark background. Absorption works in reverse, with photons of exactly the right energy lifting electrons to higher levels, leaving dark lines in a continuous spectrum. The line pattern is unique to each element, which is how the composition of stars is identified.

The Standard Model

The Standard Model groups fundamental particles into quarks and leptons. Protons and neutrons are not fundamental: each is made of three quarks (a proton is two up and one down, a neutron is one up and two down). Leptons include the electron and the neutrino. Forces are carried by exchange particles (for example the photon for the electromagnetic force). For WACE you should recognise that everyday matter is built from up quarks, down quarks and electrons, and that antiparticles exist with opposite charge.

Mass-energy equivalence

Mass and energy are interchangeable,

with $c=3.0\times10^{8}\ \text{m s}^{-1}$. Because $c^2$ is enormous, a very small mass corresponds to a very large energy. In nuclear reactions the total mass of the products is slightly less than that of the reactants, and this missing mass appears as released energy.

Mass defect and binding energy

The mass of a nucleus is less than the sum of the masses of its separate protons and neutrons. This difference is the mass defect $\Delta m$, and the energy equivalent

is the binding energy, the energy needed to pull the nucleus apart. Dividing by the number of nucleons gives the binding energy per nucleon, which peaks near iron. Nuclei lighter than iron release energy by joining together (fusion), while heavier nuclei release energy by splitting (fission), because both move toward more tightly bound products.

Nuclear reactions

In every nuclear reaction, nucleon number and charge are conserved. Radioactive decay includes alpha emission (a helium nucleus), beta emission (an electron from a neutron changing to a proton) and gamma emission (a high-energy photon as the nucleus de-excites). Fission splits a heavy nucleus into lighter fragments plus neutrons; fusion combines light nuclei. In each case the energy released equals the mass defect times $c^2$.

Choosing the right energy relationship

Decide whether a question concerns the atom (use $hf=E_i-E_f$ with energy levels) or the nucleus (use $E=\Delta m\,c^2$ with masses). Convert atomic mass units to kilograms and electronvolts to joules before substituting, and check that nucleon number and charge balance in any reaction equation.