Answer:
Half life of the sample, [tex]t_{\frac{1}{2}} = 12.15 min[/tex]
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:
[tex]N' = N(\frac{1}{2})^{\frac{t}{t_{\frac{1}{2}}}}[/tex]
Now, substituting the given values in the above mentioned formula:
[tex]\frac{1336}{1679} = (\frac{1}{2})^{\frac{4}{t_{\frac{1}{2}}}}[/tex]
[tex]0.796 = 0.5^{\frac{4}{t_{\frac{1}{2}}}}[/tex]
Taking log on both the sides:
ln(0.796) = \frac{4}{t_{\frac{1}{2}}}ln(0.5)
[tex]0.329 = 4t_{\frac{1}{2}}[/tex]
[tex]t_{\frac{1}{2}} = 12.15 min[/tex]
