The half life of Sr-90 is 28 years. hOw long will it take for a given sample of Sr-90 to be 90% decomposed?

Question

A. 93 yrs
B. 9 half lives
C. 4.3 yrs
D. 5.7x10^-3 years
E.none of the above

please explain

Answer 1

First get the rate constant (k) from the half life:
k = 0.693/(half-life) = 0.693/(28 years) = 0.02475 yrs(-1)

Then use this formula:
ln(N/No) = -k*t
where (N/No) is the ratio of material left (10% or 0.10 in this case, since it's 90% decayed), k is the rate constant from above, and t is the time.

ln(N/No)=-k*t
so, t = ln(N/No)/-k
t = ln(0.10)/-0.02475
t = -2.3025/-0.02475
t = 93 years

So, the answer is A.

Answer 2

one hl=28yrs=50%
two hl=56yrs=75%
three hl=84yrs=87.5%

The answer is a, 93 years.