# HW3-8 - 3-6 ~tomic/Nuclear Models Chap.3 In radioactive...

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Unformatted text preview: 3-6 ~tomic/Nuclear Models Chap.3 In radioactive beta decay,the number of nucleonsA remains constant although the individual number of neutrons and protons change. Members of a such beta-decay chain are isobars with nearly equal masses.Using the atomic mass data in Appendix B, plot the mass difference [70 -~X] (in u) of the nuclei Z £; th . b h .70 K 70 70 7°As 70 70 70 7O B S aaZC versus or e ISOar c am 36 r, 35 r, 34 e, 33 , 32 e, 31 a, 30 n, 29 u, ~gNi,and ~~Co. Compare the position of maximum nuclear stability with that predicted by Eq. (3.18). Solution: The liquid drop model gives the most stable proton number for a given A from Eq. (3.18), namely, Z(A) = (~) 1 + (mn -~p)c2 /(4aa)1 + acA2/3/(4aa) From the text we find 4aa = 92.80 MeV, ac = 0.714MeV, and from Table 1.5 (mn -mp)c2 = 939.56533 938.27200 = 1.2933MeV. Thus for A = 70 we find - The figure below showsAp. B masses f the isotoopes that are membersof the o isobar A = 70 as well as massescalculated by the liquid drop model. In this model the massof an atom is calculated as:ix = Zmp+Nmn+Zme-BE!d/c2. Here B E!d is the nuclear binding energy as calculated by the term in braces in Eq. (3.16). A 70 70 70 70 70 70 70 70 70 70 Nuclear mass from liquid drop Z N BE(MeV) mn(MeV) 27 43 584.634 65150.020 28 42 597.668 65135.691 29 41 602.350 65129.715 30 40 609.389 65121.383 31 39 608.075 65121.402 32 38 609.117 65119.066 33 37 601.808 65125.082 34 36 596.855 65128.742 35 35 583.549 65140.758 36 34 572.600 65150.410 -0.020 model for mn(u) 69.9414 69.9260 69.9196 69.9107 69.9107 69.9082 69.9147 69.9186 69.9315 69.9418 ISOBAR A=70 Matom(u) Matom-70 69.9562 -0.04376 69.9414 -0.05860 69.9355 -0.06447 69.9271 -0.07286 69.9277 -0.07229 69.9258 -0.07425 69.9328 -0.06724 69.9372 -0.06276 69.9507 -0.04932 69.9616 -0.03841 ~ U1 U1 co -0.040 E a I f'-0.060 U1 U1 co E II > :;:; co -0.080 "Ii [1: -0.10 26 28 30 32 34 36 38 Proton number, Z July 24, 2002 8. ...
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