72) The number of half-lives (T1/2) required for a
certain amount of radioactive isotopes in a rock to reduce to 3% of its
original amount is_____
(Thanks to Chandrasekhar, ANU)
Solution:
We know that the \frac{N}{N_{0}}=e^{-\lambda
t}---------------(1)
Given that \frac{N}{N_{0}}=3% = 0.03
By substituting
the above value in equation (1) w get
\frac{N}{N_{0}}=e^{-\lambda
t}
0.03=e^{-\lambda t}
\ln(0.03)=-\lambda t
\lambda t=3.506
\frac{0.693}{t_{1/2}}
\times t=3.506
t=\frac{3.506}{0.693}t_{1/2}
t=5.059t_{1/2}
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