Answer: 7.71 grams
Explanation:
Half-life of strontium-90 = 28 years
First we have to calculate the rate constant, we use the formula :
[tex]k=\frac{0.693}{28\text{years}}[/tex]
[tex]k=0.02475\text{years}^{-1}[/tex]
Now we have to calculate the age of the sample:
Expression for rate law for first order kinetics is given by:
[tex]t=\frac{2.303}{k}\log\frac{a}{a-x}[/tex]
where,
k = rate constant = [tex]0.02475\text{years}^{-1}[/tex]
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
[tex]174=\frac{2.303}{0.02475}\log\frac{50}{a-x}[/tex]
[tex](a-x)=7.71g[/tex]
Thus amount left after 174 years is 7.71 grams.
