Answer: Half life of Sr-90 is 29.1 years.
Explanation: Half life is the time in which the substance remains halve of its original amount. Let's say originally we have 100 grams of Sr-90. From given information, it remains one-fourth of its original amount in 58.2 years.
One-fourth of 100 gram will be 25 gram. The equation used for solving this type of problems is:
[tex]\frac{N}{N_0}=(0.5)^n[/tex]
where, n is the number of half lives, [tex]N_0[/tex] is the original amount of the radioactive substance and N is the remaining amount.
From above information:
[tex]N_0[/tex] = 100
N = 25
Let's plug in these values in the equation and find out the value of n.
[tex]\frac{25}{100}=(0.5)^n[/tex]
[tex]\frac{1}{4}=(0.5)^n[/tex]
[tex]0.25=(0.5)^n[/tex]
[tex](0.5)^2=(0.5)^n[/tex]
n = 2
From above calculations, the value of n is 2 means there are two half lives.
From the given time and the value of n, we can calculate the half life of the substance using the equation:
half life = [tex]\frac{T}{n}[/tex]
(Where T stands for time)
Let's plug in the values in the equation:
half life = [tex]\frac{58.2years}{2}[/tex]
half life = 29.1 years
So, half life of Sr-90 is 29.1 years.
