Question
Download Solution PDFA 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) ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept
Half-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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