Question:
Polonium has a half-life of $140$ days. If we take $20\,g$ of polonium initially then the amount of it that remains after $280$ days is
Polonium has a half-life of $140$ days. If we take $20\,g$ of polonium initially then the amount of it that remains after $280$ days is
Updated On: Jun 6, 2024
- 2.5 g
- 5 g
- 10 g
- 15 g
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The Correct Option is B
Solution and Explanation
After n-half lines, quantity of radiatioactive substance left is
$N=N_{0}\left(\frac{1}{2}\right)^{t / T_{1 / 2}}$
Given, $T_{1 / 2}=140$ days,
$t=28$ days, $N_{0}=20\, g$
$\therefore N=20\left(\frac{1}{2}\right)^{\frac{280}{140}}$
$=\frac{20}{4}=5\, g$
$N=N_{0}\left(\frac{1}{2}\right)^{t / T_{1 / 2}}$
Given, $T_{1 / 2}=140$ days,
$t=28$ days, $N_{0}=20\, g$
$\therefore N=20\left(\frac{1}{2}\right)^{\frac{280}{140}}$
$=\frac{20}{4}=5\, g$
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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
