Question

Please help. How do I start this?
Radium-221 has a half-life of 30 sec. How long will it take for 96% of a sample to decay?

Answer 1

First you have to find how many half-lifes it will take for 96% of a sample to decay.

96% to decay meaning you are left with 4% of the sample, equivalent to 4/100 = 1/25.

(1/2) ^ n = 1/25

Where n = number of half-lives.

To explain that above equation. note that when n=1, after one half-life, you decay half of it leaving 1/2.

When n=2, after 2 half-life, (1/2)^2 = 1/4.

Thus if you notice the above equation is actually stating the amount of sample i would get after n amount of half-lifes.

Solve for n in that equation.

(1/2) ^ n = 1/25

log 2 ^ n = log 25

n = log 25/ log 2
= 4.644 ( 4sf).

Time taken = number of half-live * duration of a half-life
= 4.644 * 30 = 139.32 = 139 sec ( 3 sf) approx.

Answer 2

Thank you so much!

Answer 3

Np.