# A range of radioactive decay calculations and solutions

1. A source has a half-life of 12 hours and an initial activity of 10mCi. After 4 days what is its activity?

2. Calculate the % of activity remaining in a source after 10 half lives.

3. a. A radionuclide decays 1% in one day. Calculate the half life.

b. A radionuclide decays 70% in one day. Calculate the half life.

4. A sample of 10.0 mCi of radioisotope decays 1.2 % in a single day

a. What is the activity after one day?

b After 30 days?

5. A sample of Cs- 137 initially contains 1000 atoms. How many Cs- 137 atoms does the sample contain after 2 years?

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#### Solution Preview

I am not supposed to deliver exact solutions but only guidance so will leave it with you to use the formulas and expression I have shown in the attachment to find the exact solutions. Hopefully you should be able to follow this to see how it all fits together to arrive at the required depth of solutions.

1. A source has a half-life of 12 hours and an initial activity of 10mCi. after 4 days what is its activity?

Well as you may see the half life mentioned of 12 hours (0.5 days) is a integer divisor of 4 days; thus we basically identify that 0.5 days goes into 4 days by 8 times

We therefore use the fact that For every half life that passes we measure half the activity of the sample . As 8 half lives pass by in the duration of 4 days passing the activity after 4 days is the initial measured activity 10mCi multiplied by (0.5)^8

2. ...

#### Solution Summary

This solution provides an in depth presentation to forming solutions for radioactive decay type questions using the radioactive decay law and half life data