HW14-14b14c-15

HW14-14b14c-15 - 7-9 The proton energy with the same speed...

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Unformatted text preview: 7-9 The proton energy with the same speed as a 10-MeV alpha particle is, thus, Ep = Ea/4 = 2.5 MeV. Then from rule 3 on page 196 for particles of the same speed in the same medium, we have Ra(lO MeV) Rp(2.5 MeV) ma z~ -14 ~~ - ~! --2 mp ZQ = 1, Thus the range of the alpha particle is RCt(lOMeV) = n,;(2.5 MeV) = 0.00567 cm (from part (b). 15. Estimate the range of a IO-MeV tritium nucleus in air. Solution: First find the kinetic energy of a proton with the same speed as a IO-MeV triton. Classical mechanics,appropriate for these energies,gives -= Et Ep (1/2)mpv; (1/2)mtvt 2 = -= mt mp -. 3 1 The proton energy with the same speed as a la-MeV triton is, thus, Ep = Et/3 = 3.333 MeV. Now find the range in air of a 3.333-MeV proton using the empirical formula of Eq. (7.47) and the data in Table 7.2. With x = IOglO .333 = 0.5229 3 pRp(3.333 MeV) = 10-2.5207+1,3729:1:+0,21045:1:2 0.01798 gfcm2, = For air at STP p = 0.0012 gfcm3, and hence Rp(3.333 MeV) = 14.98 cm. Finally, we use rule 3 on page 196 for the range of different charged particles of the same speed in the samemedium: range of the triton is then Rt(lO MeV) = 3Rp(3.333 MeV) = 44.9 cm. July 24, 2002 The ...
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