{"product_id":"atom-smashers-sticker-sheet","title":"Atom Smashers Pixel Sticker Sheet – 12 Physics Stickers","description":"\u003cp\u003e12 pixel-art physics stickers on one A5 (5.83″ × 8.27″) white kiss-cut sheet: Atom Smashers. Every character below has its own sticker page with the full physics panel.\u003c\/p\u003e\u003ch3\u003e\u003ca href=\"https:\/\/pixelatedphysics.com\/products\/lise-meitner-sticker-split-happens-physics-sticker\"\u003eLise Meitner\u003c\/a\u003e\u003c\/h3\u003e\u003cp\u003eWhen 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.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eQ = (M\u003csub\u003einitial\u003c\/sub\u003e − M\u003csub\u003efinal\u003c\/sub\u003e)c²\u003c\/strong\u003e\u003cbr\u003eQ: 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)\u003c\/p\u003e\u003ch3\u003e\u003ca href=\"https:\/\/pixelatedphysics.com\/products\/hideki-yukawa-sticker-heavy-ball-short-game-physics-sticker\"\u003eHideki Yukawa\u003c\/a\u003e\u003c\/h3\u003e\u003cp\u003eYukawa proposed that nuclear forces come from exchanging a massive particle, so they fade out exponentially beyond a range of about ħ\/mc. Turning the observed short range around predicted the mass of the carrier, later identified as the pion.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eV(r) = −(g²\/4π) e\u003csup\u003e−r\/R\u003c\/sup\u003e\/r, R = ħ\/(mc)\u003c\/strong\u003e\u003cbr\u003eV(r): potential energy between two nucleons (J); g: coupling strength (g²\/4π has units of energy times length here) (J^(1\/2)·m^(1\/2)); r: separation (m); R: range of the force (m); λ: Yukawa's range parameter, the inverse of R (he took 5×10¹² per centimetre) (m⁻¹); ħ: reduced Planck constant (J·s)\u003c\/p\u003e\u003ch3\u003e\u003ca href=\"https:\/\/pixelatedphysics.com\/products\/maria-goeppert-mayer-sticker-a-full-floor-is-magic-physics-sticker\"\u003eMaria Goeppert Mayer\u003c\/a\u003e\u003c\/h3\u003e\u003cp\u003eProtons 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.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eE\u003csub\u003eN\u003c\/sub\u003e = ħω(N + 3\/2)\u003c\/strong\u003e\u003cbr\u003eE_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)\u003c\/p\u003e\u003ch3\u003e\u003ca href=\"https:\/\/pixelatedphysics.com\/products\/moderon-neutron-moderation-pixel-sticker\"\u003eModeron\u003c\/a\u003e\u003c\/h3\u003e\u003cp\u003eA neutron loses the largest share of its energy when it hits a nucleus of about its own mass. The average logarithmic energy loss per collision tells you how many collisions a moderator needs to slow fission neutrons down to thermal energies.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eα = ((A − 1)\/(A + 1))²\u003c\/strong\u003e\u003cbr\u003eA: mass of the target nucleus in neutron masses (hydrogen: 1); α: smallest possible ratio of neutron energy after to before one collision (a head-on hit); ξ: average loss of ln E per collision (hydrogen: 1); n_(coll): average number of collisions to slow a neutron to thermal; E₀: starting neutron energy, about 2 MeV from fission (MeV); E_(th): thermal neutron energy, about 0.025 eV (eV)\u003c\/p\u003e\u003ch3\u003e\u003ca href=\"https:\/\/pixelatedphysics.com\/products\/vevette-higgs-field-pixel-sticker\"\u003eVevette\u003c\/a\u003e\u003c\/h3\u003e\u003cp\u003eThe Higgs field's potential has its lowest point away from zero, so the field takes a nonzero value v of about 246 GeV everywhere. Particles that interact with it gain masses proportional to that value and their coupling strength.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eV(φ) = −μ²|φ|² + λ|φ|⁴\u003c\/strong\u003e\u003cbr\u003eV: Higgs potential (energy density; natural units) (GeV⁴); φ: Higgs field; on the art the horizontal axis is the field's size (natural units) (GeV); μ²: parameter of the potential, positive (GeV²); λ: self-coupling of the field, positive; ⟨φ⟩: vacuum expectation value: where the field settles, in the valley (GeV); v: electroweak scale, about 246.22 GeV (GeV)\u003c\/p\u003e\u003ch3\u003e\u003ca href=\"https:\/\/pixelatedphysics.com\/products\/cptera-cpt-theorem\"\u003eCptera\u003c\/a\u003e\u003c\/h3\u003e\u003cp\u003eFlip 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.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eCPT: C × P × T is an exact symmetry\u003c\/strong\u003e\u003cbr\u003eC: charge conjugation, particle ↔ antiparticle; P: parity, mirror reflection of space; T: time reversal\u003c\/p\u003e\u003ch3\u003e\u003ca href=\"https:\/\/pixelatedphysics.com\/products\/weinberga-weak-mixing-angle\"\u003eWeinberga\u003c\/a\u003e\u003c\/h3\u003e\u003cp\u003eIn the electroweak theory (Glashow, Weinberg, Salam), the neutral gauge fields B and W³ mix. Rotating them by the weak mixing angle θ\u003csub\u003eW\u003c\/sub\u003e gives the massless photon and the massive Z boson. The angle also links the couplings: e = g sin θ\u003csub\u003eW\u003c\/sub\u003e.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003esin²θ\u003csub\u003eW\u003c\/sub\u003e ≈ 0.231 (MS-bar at M\u003csub\u003eZ\u003c\/sub\u003e)\u003c\/strong\u003e\u003cbr\u003eθ\u003csub\u003eW\u003c\/sub\u003e: weak mixing (Weinberg) angle, about 28.7°; MS-bar: modified minimal-subtraction renormalisation scheme; M\u003csub\u003eZ\u003c\/sub\u003e: Z boson mass scale, about 91.19 GeV\u003c\/p\u003e\u003ch3\u003e\u003ca href=\"https:\/\/pixelatedphysics.com\/products\/massratio-proton-electron\"\u003eMassratio\u003c\/a\u003e\u003c\/h3\u003e\u003cp\u003eThe proton is about 1836 times heavier than the electron. This dimensionless ratio sets why atoms have a tiny heavy nucleus with a light electron cloud, why nuclei barely move in chemistry (the Born–Oppenheimer approximation), and the ratio of vibrational to electronic energies in molecules. It is measured with Penning-trap mass comparisons and precision spectroscopy of molecular hydrogen ions such as HD⁺.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eμ = m\u003csub\u003ep\u003c\/sub\u003e\/m\u003csub\u003ee\u003c\/sub\u003e = 1836.152 673 426(32)\u003c\/strong\u003e\u003cbr\u003eμ: proton-to-electron mass ratio (dimensionless); m\u003csub\u003ep\u003c\/sub\u003e: proton rest mass, measured; m\u003csub\u003ee\u003c\/sub\u003e: electron rest mass, measured; (32): standard uncertainty in the last two digits, about 1.7 × 10⁻¹¹ relative\u003c\/p\u003e\u003ch3\u003e\u003ca href=\"https:\/\/pixelatedphysics.com\/products\/splitterra-cockcroft-walton\"\u003eSplitterra\u003c\/a\u003e\u003c\/h3\u003e\u003cp\u003eIn 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.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003ep + ⁷Li → 2α + 17.3 MeV\u003c\/strong\u003e\u003cbr\u003ep: proton; ⁷Li: lithium-7 nucleus; α: alpha particle, a helium-4 nucleus\u003c\/p\u003e\u003ch3\u003e\u003ca href=\"https:\/\/pixelatedphysics.com\/products\/fogplate-becquerel\"\u003eFogplate\u003c\/a\u003e\u003c\/h3\u003e\u003cp\u003eHenri Becquerel suspected that uranium salts, made to glow by sunlight, might give off X-rays. Paris stayed cloudy in late February 1896, so he put plates wrapped in black paper, with uranium salt on top, in a drawer. On 1 March he developed them anyway and found strong images: the uranium emitted penetrating rays with no sunlight at all (Comptes rendus 122, 501, 1896). It was radioactivity.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003euranium → rays, no light needed\u003c\/strong\u003e\u003cbr\u003euranium salt: potassium uranyl sulfate in his first tests; plate: photographic plate wrapped in black paper\u003c\/p\u003e\u003ch3\u003e\u003ca href=\"https:\/\/pixelatedphysics.com\/products\/helicita-goldhaber-neutrino-helicity\"\u003eHelicita\u003c\/a\u003e\u003c\/h3\u003e\u003cp\u003eIn 1958 Maurice Goldhaber, Lee Grodzins and Andrew Sunyar measured the handedness of the neutrino (“Helicity of Neutrinos”, Phys. Rev. 109, 1015). Europium-152m captures an electron and emits a neutrino; the daughter nucleus recoils and then emits a gamma ray. Selecting gammas emitted against the recoil and measuring their circular polarisation with magnetised iron tied the neutrino's spin to its motion. Neutrinos turned out left-handed: spin opposite to motion.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eh = −1\u003c\/strong\u003e\u003cbr\u003eh: helicity, the spin component along the direction of motion, in units of the maximum\u003c\/p\u003e\u003ch3\u003e\u003ca href=\"https:\/\/pixelatedphysics.com\/products\/penninga-penning-trap\"\u003ePenninga\u003c\/a\u003e\u003c\/h3\u003e\u003cp\u003eEarnshaw's theorem says no arrangement of static electric charges alone can hold a charge in stable equilibrium. A Penning trap gets around it by adding a strong, uniform magnetic field to an electric quadrupole field. A trapped particle then has three motions: a fast modified cyclotron circle (ω\u003csub\u003e+\u003c\/sub\u003e), an axial bounce along the field (ω\u003csub\u003ez\u003c\/sub\u003e), and a slow magnetron drift (ω\u003csub\u003e−\u003c\/sub\u003e). L. S. Brown and G. Gabrielse showed that, even in an imperfect trap, the three combine to give the true cyclotron frequency (“Geonium theory”, Rev. Mod. Phys. 58, 233, 1986).\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eω\u003csub\u003ec\u003c\/sub\u003e² = ω\u003csub\u003e+\u003c\/sub\u003e² + ω\u003csub\u003ez\u003c\/sub\u003e² + ω\u003csub\u003e−\u003c\/sub\u003e²\u003c\/strong\u003e\u003cbr\u003eω\u003csub\u003ec\u003c\/sub\u003e: free-space cyclotron frequency, qB\/m (rad\/s); ω\u003csub\u003e+\u003c\/sub\u003e: modified cyclotron frequency (rad\/s); ω\u003csub\u003ez\u003c\/sub\u003e: axial frequency (rad\/s); ω\u003csub\u003e−\u003c\/sub\u003e: magnetron frequency (rad\/s)\u003c\/p\u003e","brand":"Printify","offers":[{"title":"White \/ Kiss-Cut \/ 5.83″ × 8.27″","offer_id":50966992552039,"sku":"23827837638882759772","price":19.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/9510169551877603359_2048.jpg?v=1793676525","url":"https:\/\/pixelatedphysics.com\/products\/atom-smashers-sticker-sheet","provider":"Pixelated Physics","version":"1.0","type":"link"}