Atomic structure

$$A = Z + N \qquad {}^{A}_{Z}X$$ $A$ = mass number, $Z$ = atomic number (protons), $N$ = neutrons.

Radioactive decay

• $\alpha$-decay: $\ {}^{A}_{Z}X \to {}^{A-4}_{Z-2}Y + {}^{4}_{2}\text{He}$. $\quad\beta$-decay: $\ {}^{A}_{Z}X \to {}^{A}_{Z+1}Y + {}^{0}_{-1}e$. $$N = N_0\left(\frac{1}{2}\right)^{n} \qquad n = \frac{t}{T_{1/2}} \qquad \text{Fraction remaining} = \left(\tfrac{1}{2}\right)^{t/T_{1/2}}$$ $$\text{Activity } A = \lambda N \qquad T_{1/2} = \frac{0.693}{\lambda}$$

Photons and the photoelectric effect

$$E = hf = \frac{hc}{\lambda} \qquad hf = \phi + \tfrac{1}{2}mv_{\max}^2 \qquad \phi = hf_0$$ $h = 6.63\times10^{-34}$ J s, $c = 3.0\times10^{8}$ m/s, $1\ \text{eV} = 1.6\times10^{-19}$ J.

X-rays

$$eV = \tfrac{1}{2}mv^2 \quad\text{(energy of electrons accelerated through a p.d. } V\text{)}$$ $$\text{Maximum photon energy} = eV = \frac{hc}{\lambda_{\min}}$$