Modern Physics Reference Card: Formulas & Constants

PH365, AY23-2 Modern Physics Reference Card (PRC) v1.0 Special Relativity 𝑥 𝛾 𝑥 𝑣𝑡 , 𝑦 𝑇 1 𝑢 ∆𝑥 𝐸 𝑔 𝑥 𝐸 𝐸 𝑝 𝑐 𝛾𝑚𝑐 𝑚𝑣 𝑒𝑉 1 𝜆 𝑍 𝑅 𝑖ℏ 𝑛 𝑛 𝜕 𝜕𝑥 𝐿⃑ ℏ ℓ ℓ 1 𝐿 𝑚ℓ ℏ 𝑆⃑ ℏ 𝑠 𝑠 1 𝑆 𝑚 ℏ 𝑠 ℏ 𝜕 2𝑚 𝜕𝑥 𝐾 𝐽⃑ |ℓ 𝑗 𝑆⃑ 𝐿⃑ 1, 2, 3, … 0, 1, 2, … 1 𝑉 sin k 𝐿 4𝐸 𝐸 𝑉 1 𝑉 sinh 𝜅𝐿 𝐸 4𝐸 𝑉 𝑍 𝜆 ℎ𝑓 cos 𝜃 1 𝑛 𝐽⃑ 𝑠| ℏ 𝑗 𝑗 1 Special Topics 𝑣∗ 𝜔 𝑣̅ 𝑅 2𝑚 𝐸 ℏ k for 𝐸 𝐴 exp 𝐹 for 𝐸 1 𝑉 𝑣 𝑉 𝑉 𝜓 ℓ ℓ 𝑟, 𝜃, 𝜙 𝑛 𝐸 2𝑚 𝑉 ℏ 𝐸 ⟨𝑟⟩ ℎ 𝑝 ℎ𝑐 𝜆 𝑟 𝑌ℓ ℓ 𝑟𝑃 𝑟 ℓ 𝑟 |𝑅 ℓ 𝜃, 𝜙 𝐵 𝑋 𝑁𝑚 𝑅 1 ℏ𝜔 2 𝑛 𝑍𝑀 H 𝑡 𝑁𝑒 𝑄 𝑄 ln 2 𝜆 / 𝑀 𝑋 𝑀 𝑀 𝑋 𝑐 𝑑𝑁 𝑡 𝑑𝑡 𝜆𝑁 𝑡 𝑁 𝑡 𝑟 | Quantum Numbers: 𝑛 1, 2, 3, … ℓ 0, 1, 2, 3, … , 𝑛 1 𝑚ℓ 0, 1, 2, 3, … , ℓ 𝑚 𝑔 𝐸 𝐹 Nuclear Physics 𝑟 𝑑𝑟 ℓ 1/𝑘𝑇 1 𝐸 ℏ ℓ ℓ 1 2𝐼 𝐸 𝑟 sin 𝜃 𝑑𝑟 𝑑𝜃 𝑑𝜙 𝑑𝜏 𝑃 ℓ 𝛽 exp 𝛽 𝐸 𝑇 𝜅 𝑅 𝛽𝐸 1 𝐹 Hydrogen Atom 13.6 eV 𝑛 ℏ𝜔 𝑇 𝜙 𝑛 𝑎 𝑍 𝐸 𝑝𝑐 𝑇 m⋅K ℎ𝑓 1 𝑛ℓ 𝑟 𝐸 10 ℎ 1 𝑚𝑐 𝜆 𝜕 𝜕𝑡 ℏ𝜔 𝜖𝜎𝑇 2.898 𝜆 𝑝̂ g 4 𝑚 𝑐 𝑇 Δ𝜆 Ψ ∗ 𝑄 Ψ 𝑑𝑥 𝜋 ℏ 2𝑚𝐿 𝑛 𝑛 𝐸 Wave-Particle Duality 𝜆 𝑖ℏ 𝐸 𝑚𝑐 𝑚𝑐 𝑅 Ψ ∗ Ψ 𝑑𝑥 𝑔 𝑥 f 3 Name: K L M N O n 1 2 3 4 5 subshell capacity: 2 2ℓ 1 selection rules: Δℓ 1 Δ𝑚ℓ 0, 1 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p 7s 5f 6d 7p 1 𝑏 Shell Notation s p d 0 1 2 Name: ℓ 𝐸𝜓 𝑥 𝑐 ∆𝑡 𝛾𝑚𝑐 𝐸 𝑥 𝛾𝑚𝑢⃑ 𝑝⃑ 𝑉 𝑥 𝜓 𝑥 ⟨𝑄⟩ 1 𝛽 𝑓 1∓𝛽 𝑓 𝐾 𝑃 𝑎 ℏ Δ𝐸Δ𝑡 Ψ ∗ Ψ 𝑑𝑥 𝛽 𝑣 𝑣𝑢 𝑐 1 ∆𝑠 ℏ 𝑑 𝜓 𝑥 2𝑚 𝑑𝑥 𝐿 𝛾 𝐿 𝛾𝑇 ℏ Δ𝑝 Δ𝑥 1 𝛾 𝑢 𝑧 𝑣𝑥 𝑐 𝑣 𝑐 𝛽 𝑦, 𝑧 𝛾 𝑡 𝑡 Atomic Physics Quantum Physics 𝑀 𝜏 𝑀 𝑀 1 𝜆 𝑀 𝑐 𝑀 𝑐 PH365, AY22-1 Modern Physics Reference Card (PRC) v1.0 Physical Constants and Conversion Factors Quantity alpha particle mass Symbol 𝑚 angstrom atomic mass unit (amu) Avogadro constant Bohr magneton Å u 𝑁 deuteron mass 𝑒ℏ 2𝑚 4𝜋𝜀 ℏ 𝑎 𝑚 𝑒 k ℎ 𝜆 𝑚 𝑐 1 𝑘 4𝜋𝜀 𝑚 electron mass 𝑚 electron-volt elementary charge helium atomic mass hydrogen atomic mass neutron mass eV e 𝑚 𝑚 𝑚 Bohr radius Boltzmann constant Compton wavelength Coulomb constant nuclear magneton 𝜇 𝑒ℏ 2𝑚 𝜇 permeability of vacuum permittivity of vacuum Planck constant 𝜇 (multiplied by c) reduced Planck constant ℎ𝑐 ℏ ℎ/2𝜋 𝜀 ℎ (multiplied by c) proton mass ℏ𝑐 𝑚 Rydberg constant 𝑅 𝑅 c speed of light in vacuum Stefan-Boltzmann constant 𝜎 Value 6.6447  10-27 kg 4.00151 u 3727.37941 MeV/c2 10-10 m 1.66054  10-27 kg 931.494 MeV/c2 6.0221  1023 mol-1 9.2740  10-24 J/T 5.7884  10-5 eV/T 5.2918  10-11 m 1.380649  10-23 J/K 2.4263  10-12 m 8.9876  109 Nm2/C2 3.3436  10-27 kg 2.01355 u 1875.61 MeV/c2 9.1094  10-31 kg 5.4858  10-4 u 0.51100 MeV/c2 1.6022  10-19 J 1.6022  10-19 C 4.002603 u 1.007825 u 1.6749  10-27 kg 1.00866 u 939.57 MeV/c2 5.0508  10-27 J/T 4π × 10-7 N/A2 8.8542  10-12 C2/(Nꞏm2) 6.6261  10-34 Js 4.1357  10-15 eVs 1239.8 eVnm 1.0546  10-34 Js 6.5821  10-16 eVs 197.33 eVnm 1.6726  10-27 kg 1.00728 u 938.27 MeV/c2 1.09678  107 m-1 1.09737  107 m-1 2.9979  108 m/s 5.6704  10-8 W/(m2K4)

Modern Physics Reference Card: Formulas & Constants

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