Question

A sample of Strontium-90 is found to have decayed to one-fourth of its original amount after 58.2 years. What is the half-life of strontium-90?

Answer 1

The half-life of strontium-90 is 28.8 years.

Answer 2

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:

$\frac{N}{N_0}=(0.5)^n$

where, n is the number of half lives, $N_0$ is the original amount of the radioactive substance and N is the remaining amount.

From above information:

$N_0$ = 100

N = 25

Let's plug in these values in the equation and find out the value of n.

$\frac{25}{100}=(0.5)^n$

$\frac{1}{4}=(0.5)^n$

$0.25=(0.5)^n$

$(0.5)^2=(0.5)^n$

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 = $\frac{T}{n}$

(Where T stands for time)

Let's plug in the values in the equation:

half life = $\frac{58.2years}{2}$

half life = 29.1 years

So, half life of Sr-90 is 29.1 years.