Answer : The time required for decay is, 84 days.
Explanation :
Half-life of chromium-51 = 28 days
First we have to calculate the rate constant, we use the formula :
[tex]k=\frac{0.693}{t_{1/2}}[/tex]
[tex]k=\frac{0.693}{28\text{ days}}[/tex]
[tex]k=0.0248\text{ days}^{-1}[/tex]
Now we have to calculate the time required for decay.
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
t = time taken by sample = ?
a = let initial activity of the sample = 100
a - x = amount left after decay process = 12.5
Now put all the given values in above equation, we get
[tex]t=\frac{2.303}{0.0248}\log\frac{100}{12.5}[/tex]
[tex]t=83.9\text{ days}\approx 84\text{ days}[/tex]
Therefore, the time required for decay is, 84 days.
