For an unknown sample of the experiment, students measure 1668 counts when they first receive their sample and 1330 counts 5 minutes later. Calculate the half-life t1/2 t 1/2 of their sample.

15.29 minutes

Explanation:

We are given;

Original number of counts = 1668 counts New number of counts = 1330 counts Time is 5 minutes

We are required to determine the half life of the sample;

We know that half life is the time it takes for a radioactive sample to decay by a half of the original amount. To calculate the remaining mass after decay we use the formula; N = N₀ * 0.5^n, where N is the remaining amount, N₀ is the original amount and n is the number of half lives. Using the formula we can calculate the value of n; Therefore;

1330 counts = 1668 counts * 0.5^n

Thus,

0.5^n = 0.79736

Introducing logarithm;

n log 0.5 = log 0.79736

Thus,

n = 0.327

But, n = time : half life

Thus,

Half life = time : n

= 5 minutes : 0.327

= 15.29 minutes

Thus, the half life of the unknown sample is 15.29 minutes