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7”, 1. A proton (mass 938. 3 MeV/cz) or a neutron (mass 93906 MeV/C2) can sometimes ‘violate’
Econservation of energy by emitting and then reabsorbing a 7r° meson (mass 135 0 MeV/ C This 777117 is possible as long as the 7r° is reabsorbed within a short enough time, At, consistent with the E 7E7 Euncertainty principle 1 1 7,1 .1 __ ( ) Consider p ~+ p + 7r0. By what amount, AE, is energy conservation violated? (Ignore any
kinetic energies.) E 1
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% _, (b) For how long a time At, can the 7r0 meson exist? (C) Assuming the 7T0 to travel at very nearly the speed of light how far from the proton can itEA“-E“A”;““r“ go? (This procedure gives us an estimate of the range of the nuclear force, because we believe that 1 protons and neutrons are held together in the nucleus by exchanging 7r mesons. f .1 1
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Ha photon? 48Ti.
is.» S a lifetime of 1.4 ps, the lower state 3.0 ps. What is the fractional uncertainty AE / E in the energy of 1.3117—MeV gamma rays connecting the two states? lilirilr til: + 1i...» 1;. -,., siL..l..§w_ila+ . What is the Weinty in the energy of the S. If??? 33. . _ all: L, 10“8 __3
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, a) One example is the decay between two excited states of the nucleus ( ‘ 3. The decay of excited states in atoms and nuclei often leavee the system in another, albeit - lower—energy, excited state. . iilnwiilt.liifsiighilit its; 1.. , fainother example is the H0 line of the hydrogen Balmer series. In this case the lifetime of both ll,:,.,.ilv " .lliwlii . . .sizmisll,w,..iliian..ll1 ,..?Ax $32.? 5... ,..-ti , ,
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l a..- ram». _,- W New“; 2. A particle of mam :11 moves in a «aria-dimensional box of length L Take the potential energy of
the particle in the box to be zero so that its total energy is its kinetic energ,p 2 / 2m. Its energy is 1
‘ quantized by the standing-wave condition n(A / 2) = L where A is the de Broglie wavelength of the ‘ particle and n is an integer W ”1;- “,2; -'
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we, yams-“ M l 3““ it” ~ (a) Show that the allowed energy levels are given by E =2E1 where E1 = h2/8mL2. “EM“ (b) Evaluate En for an electron in a box of size L = 0.1 nm and make an energy level diagram for
the states from n— — 1 to n: 5 . (c) Use Bohr’s second postulate f 2 AE / h to calculate the wavelength of electromagnetic radiation
emitted when the electron makes a transition from n 2 2 to n = 1. (d) Repeat parts (1)) and (c) for a proton in a one-dimensional box of length L = 10 15 — 1 fm.
(These are the order of magnituée of nuclear energies ) Mug. we- as...“ l ' E V
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- Fall '10
- DavidHanna
- Physics