- #1
8614smith
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Homework Statement
Calculate the half life for alpha decay of [tex] ^{208}_{82}Pb[/tex] (in years)
Homework Equations
gamow factor
transmission probability
coloumb potential
The Attempt at a Solution
[tex]B=\frac{{Z_1}{Z_2}{e^2}}{4\pi{\epsilon_0}r}=\frac{80*2*(1.6x10^{-19})^{2}}{4*\pi*8.85*10^{-12}*8.896fm}=4.106*10^{-14}[/tex]
where r = [tex]1.2(4^{1/3}+204^{1/3}) = 8.969fm[/tex]
[tex]Q=[207.976635u-203.973476u-4.002603]c^{2}=8.30664*10^{-14}Joules[/tex]
[tex]G=({2/137})({82-2}){\sqrt(\frac{2*4.0026*1.66*10^{-27}*9*10^{16}}{8.3066*10^{-14}}[{cos^{-1}}{\sqrt0.0202}-{\sqrt(0.0202)(1-0.0202)}]=11447.44[/tex]
Is it supposed to be worked out in radians? because then the answer i get is 180.427 although this doesn't seem to give a right answer for the half life either
Is the gamow factor calculation correct?