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 = +, -
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
t = τ ln2 = ln2/λ.