Question

You are using a Geiger counter to measure the activity of a radioactive substance over the course of several minutes. If the reading of 400. counts has diminished to 100. counts after 90.3 minutes, what is the half-life of this substance?

Answer 1

Answer : The half-life of this substance will be, 45 minutes.

Explanation :

First we have to calculate the value of 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 = 90.3 min

a = initial amount of the reactant = 400

a - x = amount left after decay process = 100

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

`k=(2.303)/(90.3min)\log(400)/(100)`

`k=1.54* 10^(-2)\text{ min}^(-1)`

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

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

`1.54* 10^(-2)\text{ min}^(-1)=(0.693)/(t_(1/2))`

`t_(1/2)=45min`

Therefore, the half-life of this substance will be, 45 minutes.