s8 - t E I 7” 1 A proton(mass 938 3 MeV/cz or a...

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Unformatted text preview: t : E.{ I 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 l 21 it % _, (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 1 1 i S «'1‘ 2 ism 4; mt can“ 1.1mm 11111 1755 shear: sééscrér E i1 l s X . é 1 _ i ; E i _m7‘17.7 7 7;.7M7 7777777477 7777. 7. 71 7.77. E 1’ havens woe 1 1 E E 1 ,1 E I i 1 1 f' 1 1 ;_ 1., ’T ;. i i, i E g 1 1 ‘ ‘ 5 E 3 1 1 E’ 1 1 1 , A; 1 1 1 1 1 : ‘1 1 ' ) ‘ l 1 _ , 1 1 1 . 1 1 ( : t , I I l E ‘ .7 - 71,,” _ A7 1 .1 : 3 E i 1 : 1 .I E 1 1 ‘ f I ; 1 1 1 E ’ ' I : 1 ‘ g 1 1 1 1, ‘ A, ., 7'7 :7 7 7‘77 17 .1 ..1 EL E 1 1 1 1 1 . 1 1 1 . 1 1 1 1 , 1 1 . 1 1 1 1 s 1 l i i E 1’ I 1 : 1 1 E 1 E 1 E 5 1 , _ give N, l ., 31.1%? w _ z, ,,,,,,,,, W , V 133 w c M w 3:: N 3.2%: M ~ H ‘21.: ,u l w .. M r i .29.: v » all? e, l 39.13.57 2.4.3.3., will, hell, EL},W111§M:§¥ 3AM, ii . Q .753: i a ‘ i i . ’ x 2 x t . g . t 1 - ‘ : 1 3 3 » ‘ r 2 . X I x The upper state has 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 A .i , \ _ n _ n , 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 , , rllfl " u i g z l 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; -' 1 3 ’ t -\ T .._. w ’i l 2 . 5 , . i 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 r l b 5 , ”flaws“; ,, M4; V i more N 234:;L/flww : ...
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