Answer : The time taken by the element to decay to 2 grams is, 75.2 minutes
Step-by-step explanation:
Half-life = 13 min
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}{13\text{ min}}[/tex]
[tex]k=0.0533\text{ min}^{-1}[/tex]
Now we have to calculate the time passed.
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]0.0533\text{ min}^{-1}[/tex]
t = time passed by the sample = ?
a = initial amount of the reactant = 110 g
a - x = amount left after decay process = 2 g
Now put all the given values in above equation, we get
[tex]t=\frac{2.303}{0.0533}\log\frac{110}{2}[/tex]
[tex]t=75.2\text{ min}[/tex]
Therefore, the time taken by the element to decay to 2 grams is, 75.2 minutes
