Formulas 3

Wave Optics and Modern Physics:

Wave Optics

Double slit, diffraction grating (maxima): d sinθ = mλ, m = 0, 1, 2, ...
Single slit, (minima): w sinθ = mλ, m = 1, 2, ...
Resolving power: θmin = 1.22 λ/D

Photons and matter waves

Photon energy: Ephoton = hf = hc/λ
Photoelectric effect:  Eelectron = hf - Φ
Compton scattering:  Δλ = (λf - λi) = [h/(mec)](1 - cosθ)
De Broglie relations:  p = h/λ,  E = hf
Matter waves: λ = h/p = h/√(2mE)
Uncertainty principle: Δx Δp ~ h/2π,  Δt ΔE ~ h/2π

Atoms

Orbital angular momentum:  L2 = l(l+1)ħ2,  l = 0, 1, 2, ... .

Lz = mħ,  m = -l, (-l + 1), ... ,  (l - 1), l

Electron spin: Sz = msħ, ms = +½, -½
Hydrogen-atom energies:  En = -13.6 eV/n2
Hydrogen-atom energy eigenfunctions:  4 quantum numbers:  n, l, m, ms
l < n
Atomic spectra: hf = ∆E = Ehigh - Elow

Nuclei

Nuclear binding energy:

B(Z,N) = c2(Z*mp + N*mn - Mnuc(Z,N))

B(Z,N) = c2(Z*mH + N*mn - Matom(Z,N))

Nuclear decay: N(t) = N0exp(-λt)
R(t) = R0exp(-λt)
τ = 1/λ
t½ = τ ln2 = ln2/λ.

Constants and conversions

Elementary charge qe:
Electron mass me:
Proton mass mp:
Neutron mass mn:
Planck's constant h:

Useful combination:
Conversion:

qe = 1.6 * 10-19 C
me = 9.1 * 10-31 kg
mp = 1.672 * 10-27 kg
mn = 1.674 * 10-27 kg
h = 6.63*10-34 Js = 4.14*10-15 eVs

hc = 1240 eV nm
1 eV = 1.6*10-19 J