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Key Equations

Key Equations

Wien’s displacement law λmaxT=2.898×10−3m⋅KλmaxT=2.898×10−3m⋅K
Stefan’s law P(T)=σAT4P(T)=σAT4
Planck’s constant h=6.626×10−34J⋅s=4.136×10−15eV⋅sh=6.626×10−34J⋅s=4.136×10−15eV⋅s
Energy quantum of radiation ΔE=hfΔE=hf
Planck’s blackbody radiation law I(λ,T)=2πhc2λ51ehc/λkBT−1I(λ,T)=2πhc2λ51ehc/λkBT−1
Maximum kinetic energy
of a photoelectron		 Kmax=eΔVsKmax=eΔVs
Energy of a photon Ef=hfEf=hf
Energy balance for photoelectron Kmax=hf−ϕKmax=hf−ϕ
Cut-off frequency fc=ϕhfc=ϕh
Relativistic invariant
energy equation		 E2=p2c2+m02c4E2=p2c2+m02c4
Energy-momentum relation
for photon		 pf=Efcpf=Efc
Energy of a photon Ef=hf=hcλEf=hf=hcλ
Magnitude of photon’s momentum pf=hλpf=hλ
Photon’s linear
momentum vector		 p→f=ℏk→p→f=ℏk→
The Compton wavelength
of an electron		 λc=hm0c=0.00243nmλc=hm0c=0.00243nm
The Compton shift Δλ=λc(1−cosθ)Δλ=λc(1−cosθ)
The Balmer formula 1λ=RH(122−1n2)1λ=RH(122−1n2)
The Rydberg formula 1λ=RH(1nf2−1ni2),ni=nf+1,nf+2,…1λ=RH(1nf2−1ni2),ni=nf+1,nf+2,…
Bohr’s first quantization condition Ln=nℏ,n=1,2,…Ln=nℏ,n=1,2,…
Bohr’s second quantization condition hf=|En−Em|hf=|En−Em|
Bohr’s radius of hydrogen a0=4πε0ℏ2mee2=0.529Åa0=4πε0ℏ2mee2=0.529Å
Bohr’s radius of the nth orbit rn=a0n2rn=a0n2
Ground-state energy value,
ionization limit		 E0=18ε02mee4h2=13.6eVE0=18ε02mee4h2=13.6eV
Electron’s energy in
the nth orbit		 En=−E01n2En=−E01n2
Ground state energy of
hydrogen		 E1=−E0=−13.6eVE1=−E0=−13.6eV
The nth orbit of
hydrogen-like ion		 rn=a0Zn2rn=a0Zn2
The nth energy
of hydrogen-like ion		 En=−Z2E01n2En=−Z2E01n2
Energy of a matter wave E=hfE=hf
The de Broglie wavelength λ=hpλ=hp
The frequency-wavelength relation
for matter waves		 λf=cβλf=cβ
Heisenberg’s uncertainty principle ΔxΔp≥12ℏΔxΔp≥12ℏ