I wrote a program to find the percent of each element in the decay chain for U(adsbygoogle = window.adsbygoogle || []).push({}); ^{238}after a certain amount of time. I used the Bateman equations for serial decay chain below:

[tex]

N_n(t)= \frac{N_1(t)}{\lambda_n } \sum_{i=0}^n \lambda_i \alpha_i \exp({-\lambda_i t})

[/tex]

[tex]

\alpha_i=\prod_{\substack{j=1 \\ j\neq i}}^n \frac{\lambda_j}{\lambda_j-\lambda_i}

[/tex]

I have a working program but I don't know if the numbers are right. This is the output after 4.468e9 year, the half-life of U^{238}:

U-238 50.0%

Th-234 7.38402118408e-10%

Pa-234m 2.4681490824e-14%

Pa-234 8.55341319395e-12%

U-234 0.0027474651976%

Th-230 0.000843614748358%

Ra-226 1.79287783423e-05%

Rn-222 1.17157024517e-10%

Po-218 6.59639173904e-14%

At-218 5.31967076451e-16%

Rn-218 1.24125650799e-17%

Pb-214 5.70268705015e-13%

Bi-214 4.23445792721e-13%

Po-214 5.82681270543e-20%

Tl-210 2.76622879307e-14%

Pb-210 2.4957038641e-07%

Bi-210 1.536048551e-10%

Po-210 4.2400210405e-09%

Tl-206 8.93491905013e-14%

Pb-206 49.9963907364%

I know that the 50% will be U^{238}but will 49.996% of the atoms be really be Pb^{206}? The half-life of U^{238}is very long and the next longest in the chain is more than 4 magnitudes smaller, U^{234}with a half-life of 245500 years. Does any one know if these results look about right.

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# U-238 Decay chain program

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