Question

A radioisotope has a half-life of 5.50 min and an initial decay rate of 7200 Bq. What will be the decay rate after 22 min? Show all work and include units of measure.

Answer 1

Answer: 450 Bq

Step-by-step explanation:

This problem can be solved using the Radioactive Half Life Formula:

`A=A_(o).2^{(-t)/(h)}` (1)

Where:

`A` is the final amount of radioisotope (decay rate)

`A_(o)=7200Bq` is the initial amount of the radioisotope

`t=22min` is the time elapsed

`h=5.50min` is the half life of the radioisotope

Knowing this, let's find
`A` from (1):

`A=(7200Bq).2^{(-22min)/(5.50min)}` (2)

`A=(7200Bq).2^((-4))`

`A=(7200Bq)(0.0625)` (3)

Finally:

`A=450 Bq`>>> This is the decay rate of the radioisotope

Note it is in Becquerels (Bq), which is the derived unit approved by the International System of Units for radioactivity