Question

What is the half-life of a radioisotope if a 100 g sample becomes 25 g after
18 years?

Answer 1

9 years

Step-by-step explanation:

Answer 2

Answer : The half-life of this radioisotope is,
`9\text{ years}`

Explanation :

First we have to calculate the rate constant.

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

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

where,

k = rate constant = ?

t = time passed by the sample = 18 years

a = initial amount of the reactant = 100 g

a - x = amount left after decay process = 25 g

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

`k=\frac{2.303}{18\text{ years}}\log(100g)/(25g)`

`k=0.077\text{ years}^(-1)`

Now we have to calculate the half-life, we use the formula :

`k=(0.693)/(t_(1/2))`

`t_(1/2)=\frac{0.693}{0.077\text{ years}}`

`t_(1/2)=9\text{ years}`

Therefore, the half-life of this radioisotope is,
`9\text{ years}`