# Study Notes: SAT Physics Subject Test

## Modern Physics

The energy of a photon: $\small E=hf$ (h is Planck’s constant)

de Broglie wavelength: $\small \lambda = \frac{h}{p} = \frac{h}{mv}$

Alpha decay: $\small ^{A}_{Z}X \to ^{A-4}_{Z-2}X' + ^{4}_{2}\alpha$

$\small \beta^{-}$ decay: $\small ^{14}_{6}C \to^{14}_{7}N + ^{0}_{-1}e + \vec{V_{e}}$

$\small \beta^{+}$ decay: $\small ^{17}_{9}F \to^{17}_{8}O + ^{0}_{+1}e + V_{e}$

Electron Capture: $\small ^{7}_{4}Be + ^{0}_{-1}e \to ^{7}_{3}Li + V_{e}$

Gamma decay: $\small ^{42}_{20}Ca^{*} \to ^{42}_{20}Ca + \gamma$

Radioactive decay rates: $\small A=A_{0}e^{-\lambda t}$

#### Special relativity

Postulate 1: All the laws of physcis are the same in all inertial reference frames.

Postulate 2: the speed of light in vacuum always has the same value, regardless of the motion of the source or the observer.

Relativistic factor: $\small \gamma=\frac{1}{\sqrt{1-(\frac{v}{c})^{2}}}$

Velocity: $\small v_{\text{you}}=\frac{u+v}{1+uv/c^{2}}$

Time: $\small \Delta T_{2}=\gamma \Delta T_{1}$

Length: $\small L_{2}=\frac{L_{1}}{\gamma}$

Energy: $\small KE=(\gamma -1)mc^{2}$