Quantum Physics Vol. 2 Pixel Sticker Sheet

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

Corpuscle

In 1897 J. J. Thomson crossed electric and magnetic fields over a cathode-ray beam (“Cathode Rays”, Phil. Mag. 44, 293). He tuned them so the beam ran straight, which gives its speed, v = E/B; then the deflection from one field alone gives the mass-to-charge ratio. The result was about a thousand times smaller than for the hydrogen ion, whatever the gas or electrode metal. He called the particles corpuscles: we call them electrons.

v = E/B
v: beam speed (m/s); E: electric field (V/m); B: magnetic field (T); m/e: mass-to-charge ratio of the particle (kg/C)

Dynodra

A photomultiplier tube turns one photon into a measurable pulse. The photon frees an electron from the photocathode. It is then accelerated onto the first dynode, where it knocks out several secondary electrons. Each of those is accelerated onto the next dynode, and so on. With δ secondaries per electron at each of N stages, the gain multiplies.

G = δ^N, so ln G = N ln δ
G: overall electron gain; δ: secondary-emission ratio per dynode; N: number of dynodes

Magnetonix

An electron with one unit of orbital angular momentum ħ has a magnetic moment of one Bohr magneton. This is the natural unit for atomic and electron magnetism.

μ_B = eħ/(2m_e) = 9.274 010 0657(29) × 10⁻²⁴ J/T
μ_B: Bohr magneton (J/T); e: elementary charge (exact); ħ: reduced Planck constant (exact); m_e: electron mass (measured)

Pumpette

A single-electron pump is a nanoscale island (a quantum dot or metal island) cut off by tunnel barriers. Its charging energy is large enough that electrons can only cross one at a time (Coulomb blockade). Driving the gates at frequency f moves one electron per cycle, so the current is set by counting.

I = ef
I: current (A); e: elementary charge, 1.602 176 634 × 10⁻¹⁹ C exactly; f: pumping frequency (Hz)

Quantix

In a superconducting ring the electrons pair up into Cooper pairs and share a single macroscopic wavefunction. The phase must come back to itself around the loop, so the fluxoid (the flux, plus a small supercurrent term) is quantised in whole multiples of Φ₀. In a type-II superconductor the field enters as Abrikosov vortices, each carrying one Φ₀, arranged in a triangular lattice.

Φ₀ = h/2e ≈ 2.067 833 848 × 10⁻¹⁵ Wb
Φ₀: magnetic flux quantum (Wb); h: Planck constant (exact); 2e: charge of a Cooper pair

Splitterra

In April 1932 at the Cavendish Laboratory, John Cockcroft and Ernest Walton fired protons from a high-voltage accelerator at lithium. Scintillation screens flashed with pairs of alpha particles flying apart (Proc. R. Soc. A 137, 229, 1932). It was the first nucleus split by artificially accelerated particles, and the energy released matched E = mc².

p + ⁷Li → 2α + 17.3 MeV
p: proton; ⁷Li: lithium-7 nucleus; α: alpha particle, a helium-4 nucleus

Feeblea

In 1909 a young G. I. Taylor photographed the shadow of a needle with light so dim that, in modern terms, rarely more than one photon was in the box at a time (Proc. Camb. Phil. Soc. 15, 114). His longest exposure ran about 2000 hours, roughly three months. The diffraction fringes were just as sharp as with bright light.

t_exposure ≈ 2000 h
t_exposure: exposure time of the faintest photograph

Cptera

Flip all charges (C), mirror space (P) and run time backwards (T), all at once, and any local, Lorentz-invariant quantum field theory looks exactly the same. This CPT theorem was worked out by Julian Schwinger (1951), Gerhart Lüders (1954) and Wolfgang Pauli (1955). It forces a particle and its antiparticle to have exactly equal mass and lifetime.

CPT: C × P × T is an exact symmetry
C: charge conjugation, particle ↔ antiparticle; P: parity, mirror reflection of space; T: time reversal

Dicka

N excited atoms that radiate independently give N times the light of one. But if they are packed close together, within about a wavelength, or otherwise coupled to the same light field, they can lock into phase and radiate as one giant dipole. Then the peak intensity grows as N², and the light comes out in a short, bright burst. Robert Dicke predicted this in “Coherence in Spontaneous Radiation Processes” (Phys. Rev. 93, 99, 1954).

I_peak ∝ N²
I_peak: peak emitted intensity (W); N: number of emitters radiating in phase

Hanleva

Shine polarised light at the mercury resonance line (253.7 nm) into mercury vapour and the atoms re-emit it as polarised resonance fluorescence. Add a weak magnetic field and the polarisation drops. Wilhelm Hanle reported this in “Über magnetische Beeinflussung der Polarisation der Resonanzfluoreszenz” (Z. Phys. 30, 93, 1924). The excited atoms behave like little oscillating dipoles that precess around the field at the Larmor frequency. If they turn through a large angle before they emit, the emitted light comes out with a scrambled direction of polarisation.

ΔB ≈ ħ / (g μ_B τ)
ΔB: field scale over which the polarisation falls (tesla, T); ħ: reduced Planck constant; g: Landé g-factor of the excited state; μ_B: Bohr magneton; τ: lifetime of the excited state (s)

Starka

Put atoms in a strong electric field and their spectral lines split and shift. Johannes Stark observed this in hydrogen in 1913 and published it in full in Annalen der Physik (“Beobachtungen über den Effekt des elektrischen Feldes auf Spektrallinien”, Ann. Phys. 348, 965, 1914). Antonino Lo Surdo saw it independently the same year. Hydrogen is special: states with the same n but different shapes have the same energy, so the field mixes them and the shift is proportional to the field itself, giving a symmetric pattern of components.

ΔE = (3/2) n (n₁ − n₂) e a₀ F
ΔE: energy shift of the level (J); n: principal quantum number; n₁, n₂: parabolic quantum numbers; e: elementary charge (C); a₀: Bohr radius (m); F: electric field strength (V/m)

Augermeit

Remove an electron from an atom's innermost K shell and an electron from the L shell drops into the hole. The energy released can leave as an X-ray photon. Or it can pass directly to another electron, which is ejected from the atom with a characteristic energy: an Auger electron. No photon is emitted and reabsorbed. For a KLL transition the Auger electron's energy is roughly the K binding energy minus two L binding energies, which makes it a fingerprint of the element. That is the basis of Auger electron spectroscopy.

E_KLL ≈ E_K − E_L − E_L
E_KLL: kinetic energy of the ejected Auger electron (eV); E_K: binding energy of the K-shell electron (eV); E_L: binding energies of the two L-shell electrons involved (eV)