Question:
The half life of a radioactive substance is $20\, minutes$. The time taken between $50\%$ decay and $87.5\%$ decay of the substance will be
The half life of a radioactive substance is $20\, minutes$. The time taken between $50\%$ decay and $87.5\%$ decay of the substance will be
Updated On: Sep 20, 2024
- 30 minutes
- 40 minutes
- 25 minutes
- 10 minutes
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The Correct Option is B
Solution and Explanation
Given, $ T_{1 / 2}=20 \,min $
$N_{1}=50 $
$N_{2}=100-87.5=12.5$
We know that, time taken by a substance to decay,
$t_{2}-t_{1} =\frac{T}{\ln 2} \ln \left(\frac{N_{1}}{N_{2}}\right)=\frac{20}{\ln 2} \ln \left[\frac{50}{12.5}\right] $
$=\frac{20}{\ln 2} \ln 4=40 \,min$
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Concepts Used:
Half-life
The amount of time taken for half of a particular sample to react is known as Half-life.
Half-Life Formula:
We can describe exponential decay by any of the three formulas
