Question Bank - Mathematics

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A radioactive substance decays at a rate proportional to the amount of substance present. If half of the substance decays in 100 years, then what is the decay constant (proportionality constant) ?

A.
\(\frac{\ln 2}{100}\)
B.
\(\frac{\ln 5}{100}\)
C.
\(\frac{\ln 10}{100}\)
D.
\(\frac{2 \ln 2}{100}\)

Solution:

ConceptHalf-life: \(\displaystyle t_{\frac{1}{2}}=\frac{log_e2}{k}\)Where k is the decay constant.Calculation:We know that \(\displaystyle t_{\frac{1}{2}}=\frac{log_e2}{k}\)Putting the value of t1/2 = 100 years,? 100 = \(\displaystyle \frac{log_e2}{k}\)? k = \(\displaystyle \frac{log_e2}{100}\)? Decay constant is \(\displaystyle \frac{log_e2}{100}\).

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