Atomic Spectra & Nuclear Chemistry

Spectra and Photoelectron Spectroscopy

In hydrogen $E_n = -13.6/n^2$ eV; an electron falling between levels emits a photon of energy $|\Delta E| = hf = hc/\lambda$, and absorbing the same energy lifts it back. Lyman lines end at $n = 1$ (UV), Balmer at $n = 2$ (visible). The photoelectric effect, $KE_{\max} = hf - \Phi$, shows light is quantized: intensity changes how many electrons leave, not how fast. In PES, peak position is a subshell's binding energy and peak area counts its electrons.

Nuclear Chemistry

Alpha decay lowers $A$ by 4 and $Z$ by 2; $\beta^-$ raises $Z$ by 1; $\beta^+$ and electron capture lower it by 1; gamma changes neither. Decay is first order, so $N = N_0(1/2)^{t/t_{1/2}}$. Mass defect is binding energy, $E = \Delta m c^2$. Imaging uses short-lived gamma emitters such as $^{99m}\text{Tc}$.

Key Takeaways

• Levels crowd together at high $n$, so $6 \to 5$ emits far less than $3 \to 2$.
• Conserve $A$ and $Z$ in every decay, one step of a chain at a time.
• Each half-life halves what is left.