Question

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.

Answer 1

15.29 minutes

Step-by-step 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