Question

The radioactive element strontium-90 has a half-life of 28 years. Suppose we start with a 50-g mass of strontium-90. How much will be left after 174 years? Compute the answer to three significant digits.

Answer 1

Answer: 7.71 grams

Step-by-step explanation:

Half-life of strontium-90 = 28 years

First we have to calculate the rate constant, we use the formula :

`k=\frac{0.693}{28\text{years}}`

`k=0.02475\text{years}^(-1)`

Now we have to calculate the age of the sample:

Expression for rate law for first order kinetics is given by:

`t=(2.303)/(k)\log(a)/(a-x)`

where,

k = rate constant =
`0.02475\text{years}^(-1)`

t = age of sample = 174 years

a = initial amount of the reactant = 50 g

a - x = amount left after decay process = ?

Now put all the given values in above equation, we get

`174=(2.303)/(0.02475)\log(50)/(a-x)`

`(a-x)=7.71g`

Thus amount left after 174 years is 7.71 grams.