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

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:

$t=\frac{2.303}{k}\log\frac{a}{a-x}$

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

$174=\frac{2.303}{0.02475}\log\frac{50}{a-x}$

$(a-x)=7.71g$

Thus amount left after 174 years is 7.71 grams.