Answer to Question #108496 in Atomic and Nuclear Physics for Gifty

Question #108496
Half life period of U234 is 2.5×105 years. In how many years it will remain 25% of original amount?
1
Expert's answer
2020-04-08T10:28:44-0400

"N_0" - initial amount of U234

"N=0.25 \\times N_0" - final amount of U234

"T=2.5 \\times 10^5 \\text{ years}" - half life period

We can use the fact that


"N=N_0 \\Big( {1\\over 2}\\Big)^{\\frac{t}{T}}"



"N=0.25\\times N_0=N_0 \\Big( {1\\over 2}\\Big)^{\\frac{t}{T}} \\ \\Rightarrow 0.25= \\Big( {1\\over 2}\\Big)^{\\frac{t}{T}} , \\ \\Big( {1\\over 2}\\Big)^2=\\Big( {1\\over 2}\\Big)^{\\frac{t}{T}} \\ \\Rightarrow 2=\\frac{t}{T}"

"t=2T=5.0 \\times 10^5 \\text{ years}"


Answer: in "5\\times 10^5" years it will remain 25% of original amount.


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