Question

A half-life is 4 days. How many days will pass for the 1000g sample to become 125g?

Answer with following format:

(a) Rule(s)

(b) What the rule(s) says

(c) This problems application of that or

those rules.

Answer 1

According to radioactive decay rule the numbers of radioactive nuclei decreasing exponentialy with respect to time .

If N_o be the nuclei present in a radioactive sample at t=0 and N be the nuclei present at time t. Then we can write. (N/N_o) =(1/2)ⁿ. Here n= t /t_1/2.   t_1/2=half life

So (125/1000)=(1/2)ⁿ

  (1/8)=(1/2)ⁿ. => (1/2)³=(1/2)ⁿ

so n=3 this emplys that. t/t_1/2=3

That is. t= 3*t_{1/2 .} in question t_1/2=4 days

So. t=3*4=12 days. That is 12 days to be taken to reduce 1000 gram to 125gram of given radioactive sample .