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In nuclear physics, the Geiger–Nuttall law or Geiger–Nuttall rule relates the decay constant of a radioactive isotope with the energy of the alpha particles emitted. Roughly speaking, it states that short-lived isotopes emit more energetic alpha particles than long-lived ones.
Based on wind resistance, for example, the terminal velocity of a skydiver in a belly-to-earth (i.e., face down) free-fall position is about 195 km/h (122 mph or 54 m/s). [3] This velocity is the asymptotic limiting value of the acceleration process, because the effective forces on the body balance each other more and more closely as the ...
Oresme's geometric verification of the Oxford Calculators' Merton Rule of uniform acceleration, or mean speed theorem. Galileo's demonstration of the law of the space traversed in case of uniformly varied motion. It is the same demonstration that Oresme had made centuries earlier.
From the equation for uniform linear acceleration, the distance covered = + for initial speed =, constant acceleration (acceleration due to gravity without air resistance), and time elapsed , it follows that the distance is proportional to (in symbols, ), thus the distance from the starting point are consecutive squares for integer values of time elapsed.
and are the half-lives (inverses of reaction rates in the above equation modulo ln(2)) of the parent and daughter, respectively, and BR is the branching ratio. In transient equilibrium, the Bateman equation cannot be simplified by assuming the daughter's half-life is negligible compared to the parent's half-life.
In mathematical physics, Gleason's theorem shows that the rule one uses to calculate probabilities in quantum physics, the Born rule, can be derived from the usual mathematical representation of measurements in quantum physics together with the assumption of non-contextuality.
The rule assumes the Russell–Saunders coupling and that interactions between spin magnetic moments can be ignored. The latter is an incorrect assumption for light atoms. As a result of this, the rule is optimally followed by atoms with medium atomic numbers. [4] The rule was first stated in 1923 by German-American physicist Alfred Landé. [1]
For example, renormalization in QED modifies the mass of the free field electron to match that of a physical electron (with an electromagnetic field), and will in doing so add a term to the free field Lagrangian which must be cancelled by a counterterm in the interaction Lagrangian, that then shows up as a two-line vertex in the Feynman diagrams.