Answer to Question #113806 in Atomic and Nuclear Physics for Nya

Question #113806
If the half-life of an isotope is 3 years, what fraction of the isotope remains after 4 years? (put fraction in as decimal)
1
Expert's answer
2020-05-04T12:40:05-0400

Solution. Using radioactive decay law


N(t)=N0×eλt=N0×etln2T=N0×2tTN(t)=N_0\times e^{-\lambda t}=N_0\times e^{-\frac{tln 2}{T}}=N_0\times2^{-\frac{t}{T}}

where N is the number of non-decaying isotopes; N0 is initial number of isotopes; t=4 years is time; T=3 years is half life.

Therefore, the fraction of the isotope that remains after 4 years


N(4)N0=2430.4\frac {N(4)}{N_0}=2^{-\frac{4}{3}} \approx 0.4

Answer. 0.4.


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