Atomic and Nuclear Physics: Spectra, Decay, Binding and Reactions
Discrete quantum energies explain line spectra; mass-energy and conservation laws explain nuclear stability, radioactivity and reaction energy.
Learning goals
- connect spectral lines with photon energy and atomic transitions;
- use exponential decay, activity and half-life;
- distinguish alpha, beta and gamma processes;
- calculate mass defect and nuclear binding energy;
- balance nuclear equations and interpret reaction $Q$-values.
1. Atomic energy levels and spectra
Bound electrons occupy discrete energy levels. Absorption occurs when a photon supplies exactly $E_\gamma=hf=hc/\lambda$ equal to an upward energy gap. Emission occurs when an electron moves to a lower level and releases a photon with $hf=E_i-E_f$. Because each element has its own energy-level pattern, its emission and absorption lines provide a spectroscopic fingerprint. A continuous spectrum comes from a dense range of thermal energies; isolated atoms produce line spectra.
2. Radioactive decay
Radioactive decay is spontaneous and random for an individual nucleus but statistically predictable for a large sample. The undecayed number is $N=N_0e^{-\lambda t}$, activity is $A=\lambda N$, and half-life is $t_{1/2}=\ln2/\lambda$. After $n$ half-lives, $N/N_0=(1/2)^n$. Activity is measured in becquerels, where $1\,Bq=1$ decay per second.