Physicist Portraits Vol. 2 Pixel Sticker Sheet

10 pixel-art physics stickers on one A5 (5.83″ × 8.27″) white kiss-cut sheet: Physicist Portraits Vol. 2. Every character below has its own sticker page with the full physics panel.

Christiaan Huygens

Huygens' principle treats every point on a wavefront as a source of small spherical wavelets. After a short time, the new wavefront is the surface that touches all of those wavelets, which explains reflection and refraction.

r = vΔt

r: radius of each secondary wavelet after time \Delta t (m); v: wave speed in the medium (m/s); Δ t: time step (s)

Lise Meitner

When a uranium nucleus splits, the pieces weigh less than the original, and the missing mass appears as energy. Meitner and Frisch estimated it from the electric repulsion between the two fragments at the moment they part: about 200 MeV per fission.

Q = (M_initial − M_final)c²

Q: energy released (quoted in MeV) (J); M: total rest mass before/after (kg); c: speed of light (m/s); E_C: Coulomb repulsion energy of two touching fragments (J); Z₁, Z₂: fragment proton numbers; e: elementary charge (C)

Maria Goeppert Mayer

Protons and neutrons fill energy shells in the nucleus, much like electrons in an atom. Adding strong spin-orbit coupling moves the shell gaps to the observed magic numbers 2, 8, 20, 28, 50, 82 and 126, where nuclei are unusually stable.

E_N = ħω(N + 3/2)

E_N: energy of oscillator shell N (J); N: oscillator shell number; ħω: oscillator level spacing (J); g_N: states in shell N per nucleon species (spin included); V_(ℓ s): spin–orbit potential (J); C(r): radial strength of the spin–orbit term (with orbital and spin angular momentum measured in units of ħ) (J)

Marie Curie

Each radioactive nucleus has a fixed chance per second of decaying, so the number left falls exponentially. The half-life is ln 2 divided by that decay constant, and the activity is the decay constant times the number of nuclei.

N(t) = N₀ e^(−λt)

N: number of undecayed nuclei; λ: decay constant (s⁻¹); t_(1/2): half-life (s); A: activity (1 Bq = 1 decay per second) (Bq)

C. V. Raman

Most light scattered by molecules keeps its colour, but a tiny fraction gives up or takes energy from a molecular vibration and comes out shifted. That Raman shift is a fingerprint of the molecule's vibrations.

hν_s = hν₀ − hν_vib (Stokes)

h: Planck constant (J·s); ν₀: frequency of incident light (Hz); ν_s: frequency of scattered light (Hz); ν_(vib): molecular vibration frequency (Hz); Δν̃: Raman shift in wavenumber (usually quoted per centimetre) (m⁻¹, cm⁻¹); λ₀, λ_s: incident and scattered wavelengths (m)

Max Planck

Planck found that the glow of a hot body could only be explained if energy is exchanged in packets of hν. His formula gives the full blackbody spectrum at any temperature and started quantum theory.

E = hν

E: quantum of energy (J); h: Planck constant (exact since 2019) (J·s); ν: frequency (Hz); B_ν: spectral radiance (W·m⁻²·sr⁻¹·Hz⁻¹); T: temperature (K); k_B: Boltzmann constant (J/K)

Niels Bohr

In Bohr's model the energy levels of hydrogen are minus the Rydberg energy divided by n squared. When an electron drops from a higher level to a lower one it emits a photon carrying exactly the energy difference, which explains hydrogen's sharp spectral lines.

E_n = −R_∞hc/n², with R_∞hc ≈ 13.6 eV

E_n: energy of level n (infinite-nuclear-mass approximation; hydrogen uses reduced mass; quoted in eV) (J); R_∞ hc: Rydberg energy (CODATA 2022) (J); n: principal quantum number; h: Planck constant (J·s); ν: photon frequency (Hz); Eᵢ, E_f: initial and final level energies (J)

Enrico Fermi

The Fermi–Dirac distribution gives the chance that a state of energy E is occupied by a fermion. Deep below the chemical potential states are full, far above it they are empty, and exactly at it the chance is one half.

f(E) = 1/(e^((E−μ)/(kT)) + 1)

f(E): Fermi–Dirac occupation probability; E: single-particle energy (J); μ: chemical potential (J); k: Boltzmann constant (J/K); T: temperature (K)

Richard Feynman

Feynman's rule: to get from a to b, a quantum particle takes every possible path, and each path contributes a phase set by its action. You add all those amplitudes and square the total to get the probability.

K(b,a) = Σ_paths e^(iS/ħ)

K(b,a): amplitude to go from a to b (propagator), in d spatial dimensions (m^(-d)); S: classical action along a path (J·s); ħ: reduced Planck constant (J·s); φ_k: amplitude for alternative k; P: probability

Wolfgang Pauli

Two identical fermions must have a wavefunction that changes sign when they are swapped. If both tried to occupy the same state, the wavefunction would be zero everywhere, so the arrangement is forbidden: one fermion per state.

ψ(1,2) = [φ_a(1)φ_b(2) − φ_a(2)φ_b(1)]/√2

ψ: two-particle antisymmetrised wavefunction; φₐ, φ_b: single-particle orbitals (including spin); a, b: full sets of quantum numbers (n,ℓ,m_ℓ,m_s)