Question

Strontium-90 has a half-life of 29 years. In how many years will a 1 kg sample of strontium-90 decay and reduce to 0.25 kg of strontium-90?
Answer

58 years

116 years

87 years

29 years

Answer 1

58 years.

Use this expression:
\[\ aA=Ae^{-kt} \]
Where:
A - is the initial amount (1 kg)
a - percentage of A left after time t ( 0<a<1 )
k - constant (that you can find from knowing the half-life)
t - time passed

So you know that after t=29 years there is 0.5A left. From that you can calculate k and use it to calculate how much time it takes to drop to 0.25 percent of initial amount.

It is even easier to do this if you notice that 0.25 is half of half life. So it drops by a half in 29 years and by another half in another 29 years. In each 29 years the amount halves itself. so it goes:
0 years - 1kg
29 years- 1/2*1kg
2*29years - 1/2*1/2 *1kg (this is what you are asked for)
3*29years- 1/2*1/2*1/2*1kg
4*29years -1/2*1/2*1/2*1/2*1kg