Modern Physics
Core concepts
Modern physics covers quantization, the photoelectric effect, atomic energy levels, and nuclear processes. Photon energy is $E=hf=hc/\lambda$, with $h\approx 6.63\times10^{-34},\mathrm{J,s}$ and $hc\approx1240,\mathrm{eV,nm}$. In the photoelectric effect, $K_{max}=hf-\phi$, where $\phi$ is the work function; no emission occurs below the threshold frequency $f_0=\phi/h$. Atomic spectra arise from transitions $\Delta E=hf$ between discrete levels. De Broglie wavelength is $\lambda=h/p$. Nuclear decay types: alpha (emits $^4_2$He, $Z$ drops 2, $A$ drops 4), beta-minus (neutron→proton, $Z$ rises 1), and gamma (photon, no change in $Z$ or $A$). Mass-energy equivalence: $E=mc^2$; binding energy reflects mass defect.
Traps to watch
- Intensity changes the number of photoelectrons, not their maximum kinetic energy; only frequency changes $K_{max}$.
- Converting between eV and joules ($1,\mathrm{eV}=1.6\times10^{-19},\mathrm{J}$) is a frequent error source.
- In beta decay, the atomic number changes but the mass number does not.
- Emission lines come from electrons dropping to lower levels; absorption lines from rising.
- Heavier particles have shorter de Broglie wavelengths at the same speed.
Worked example
Light of $\lambda=200,\mathrm{nm}$ strikes a metal with $\phi=2.0,\mathrm{eV}$. Photon energy: $1240/200=6.2,\mathrm{eV}$. Then $K_{max}=6.2-2.0=4.2,\mathrm{eV}$.
Rule of thumb: use $E(\mathrm{eV})=1240/\lambda(\mathrm{nm})$ to skip joule conversions in photon problems.