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:

$k=\frac{2.303}{t}\log\frac{a}{a-x}$

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

$k=\frac{2.303}{90.3min}\log\frac{400}{100}$

$k=1.54\times 10^{-2}\text{ min}^{-1}$

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

$k=\frac{0.693}{t_{1/2}}$

$1.54\times 10^{-2}\text{ min}^{-1}=\frac{0.693}{t_{1/2}}$

$t_{1/2}=45min$

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