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Key Equations

Wien’s displacement law λmaxT=2.898×103mKλmaxT=2.898×103mK
Stefan’s law P(T)=σAT4P(T)=σAT4
Planck’s constant h=6.626×1034Js=4.136×1015eVsh=6.626×1034Js=4.136×1015eVs
Energy quantum of radiation ΔE=hfΔE=hf
Planck’s blackbody radiation law I(λ,T)=2πhc2λ51ehc/λkBT1I(λ,T)=2πhc2λ51ehc/λkBT1
Maximum kinetic energy
of a photoelectron
Energy of a photon Ef=hfEf=hf
Energy balance for photoelectron Kmax=hfϕKmax=hfϕ
Cut-off frequency fc=ϕhfc=ϕh
Relativistic invariant
energy equation
Energy-momentum relation
for photon
Energy of a photon Ef=hf=hcλEf=hf=hcλ
Magnitude of photon’s momentum pf=hλpf=hλ
Photon’s linear
momentum vector
The Compton wavelength
of an electron
The Compton shift Δλ=λc(1cosθ)Δλ=λc(1cosθ)
The Balmer formula 1λ=RH(1221n2)1λ=RH(1221n2)
The Rydberg formula 1λ=RH(1nf21ni2),ni=nf+1,nf+2,1λ=RH(1nf21ni2),ni=nf+1,nf+2,
Bohr’s first quantization condition Ln=n,n=1,2,Ln=n,n=1,2,
Bohr’s second quantization condition hf=|EnEm|hf=|EnEm|
Bohr’s radius of hydrogen a0=4πε02mee2=0.529Åa0=4πε02mee2=0.529Å
Bohr’s radius of the nth orbit rn=a0n2rn=a0n2
Ground-state energy value,
ionization limit
Electron’s energy in
the nth orbit
Ground state energy of
The nth orbit of
hydrogen-like ion
The nth energy
of hydrogen-like ion
Energy of a matter wave E=hfE=hf
The de Broglie wavelength λ=hpλ=hp
The frequency-wavelength relation
for matter waves
Heisenberg’s uncertainty principle ΔxΔp12ΔxΔp12
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