Skip to ContentGo to accessibility pageKeyboard shortcuts menu
OpenStax Logo
University Physics Volume 3

Key Equations

University Physics Volume 3Key Equations
Search for key terms or text.

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
PreviousNext
Order a print copy
Citation/Attribution

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute OpenStax.

Attribution information
  • If you are redistributing all or part of this book in a print format, then you must include on every physical page the following attribution:
    Access for free at https://openstax.org/books/university-physics-volume-3/pages/1-introduction
  • If you are redistributing all or part of this book in a digital format, then you must include on every digital page view the following attribution:
    Access for free at https://openstax.org/books/university-physics-volume-3/pages/1-introduction
Citation information

© Jan 27, 2025 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.