Question

For an unknown sample of the experiment, students measure 1679 counts when they first receive their sample and 1336 counts four minutes later. Calculate the half-life t1/2of their sample.

Answer 1

Answer:

Half life of the sample, $t_{\frac{1}{2}} = 12.15 min$

Given:

Initial amount, N = 1679

Final count of amount, N' = 1336

Time elapsed, t = 4 min = 240 s

Solution:

Now, To calculate the half life, using the relation:

$N' = N(\frac{1}{2})^{\frac{t}{t_{\frac{1}{2}}}}$

Now, substituting the given values in the above mentioned formula:

$\frac{1336}{1679} = (\frac{1}{2})^{\frac{4}{t_{\frac{1}{2}}}}$

$0.796 = 0.5^{\frac{4}{t_{\frac{1}{2}}}}$

Taking log on both the sides:

ln(0.796) = \frac{4}{t_{\frac{1}{2}}}ln(0.5)

$0.329 = 4t_{\frac{1}{2}}$

$t_{\frac{1}{2}} = 12.15 min$