University Physics Volume 3

# 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 energyof 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 invariantenergy equation $E2=p2c2+m02c4E2=p2c2+m02c4$ Energy-momentum relationfor photon $pf=Efcpf=Efc$ Energy of a photon $Ef=hf=hcλEf=hf=hcλ$ Magnitude of photon’s momentum $pf=hλpf=hλ$ Photon’s linearmomentum vector $p→f=ℏk→p→f=ℏk→$ The Compton wavelengthof 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 inthe nth orbit $En=−E01n2En=−E01n2$ Ground state energy ofhydrogen $E1=−E0=−13.6eVE1=−E0=−13.6eV$ The nth orbit ofhydrogen-like ion $rn=a0Zn2rn=a0Zn2$ The nth energyof hydrogen-like ion $En=−Z2E01n2En=−Z2E01n2$ Energy of a matter wave $E=hfE=hf$ The de Broglie wavelength $λ=hpλ=hp$ The frequency-wavelength relationfor matter waves $λf=cβλf=cβ$ Heisenberg’s uncertainty principle $ΔxΔp≥12ℏΔxΔp≥12ℏ$