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Please help ASAP The half-life of cobalt-60 is 5 years. How old is a sample of cobalt-60 if only one-eighth of the original sample is still cobalt-60?

A5 years
B10 years
C15 years

D.20 years

Verified Answer :

FauxGeoDuck

C
........................

Answer:The correct answer is option C.

Explanation:

Initial mass of the sample = \(N_o\)

Sample left after t years ,=\(N=\frac{N_o}{8}\)

Half-life of sample of cobalt-60 \(t_{\frac{1}{2}}\) = 5 years

\(\lambda=\frac{0.693}{t_{\frac{1}{2}}}=\frac{0.693}{5 years}=0.1386 year^{-1}\)

\(N=N_o\times e^{-\lambda t}\)

\(ln[N]=ln[N_o]-\lambda t\)

\(\log[\frac{[N_o]}{8}]=\log[N_o]-\frac{\lambda t}{2.303}\)

\(\log[\frac{1}{8}]=-\frac{0.1386 year^{-1}\times t}{2.303}\)

\(t=15.33 years\approx 15 years\)

Hence ,the correct answer is option C.

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