A Geiger counter registers a count rate of 4,800 counts per minute from a sample of a radioisotope. Sixteen minutes later, the count rate is 1,200 counts per minute. What is the half-life of the radioisotope?

Answer : The half-life of the radioisotope is, 8.00 min

Explanation :

First we have to calculate the rate constant.

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

where,

k = rate constant = ?

t = time passed by the sample  = 16 min

a = initial amount of the reactant  = 4800

a - x = amount left after decay process = 1200

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

Now we have to calculate the half-life.

Therefore, the half-life of the radioisotope is, 8.00 min