7.10 to 7.12 answers

1.              What happens to the amount of ‘mother’ nuclei as time passes?

Decrease

2.              What sort of radioisotope will decay the fastest - one with a long half life or one with a short half life?

One with a short half life

3.              Does half life tell us exactly when a particular nucleus in a radioisotope will decay?

No.  It is a random process - we can not know exactly when a particular nucleus will decay

4.              What are the two definitions of half life?

a.                  The time taken for the activity of a sample to halve

b.                  The time taken for the number of radioactive atoms in a sample to halve

5.              What does the activity of a source mean?

The number of decays per second

6.              What is the unit of activity?

Becquerel (Bq)

7.              What will happen to the number of ‘mother’ nuclei after two half lives?

1    è    ½     è    ¼  

     1xhalf life       2xhalf life 

The number of mother nuclei will be ¼ of the original number

8.              What will happen to the activity of a source after two half lives?

1    è    ½     è    ¼  

     1xhalf life       2xhalf life 

The activity will be ¼ of the original activity

 

 

7.10 to 7.12 calculation answers

12 January 2012

10:24

1.              A radioisotope has a half life of 12 years. What fraction of the radioisotope will be left after 60 years?

Fraction remaining:

1    è    ½     è    ¼    è   1/8    è   1/16    è   1/32

1xhalf life       2xhalf life          3xhalf life        4xhalf life          5xhalf life

      12 years        24 years            36 years          48 years            60 years

 

2.              If the activity of a sample falls to 1/64th of its original level after 2 hours, what is the half life of the sample?

 

1  è  ½  è  ¼  è  1/8  è  1/16  è  1/32  è  1/64

      1xhalf life    2xhalf life     3xhalf life      4xhalf life         5xhalf life         6xhalf life

Decay takes 2 hours (= 120 minutes)

This is 6 half lives

So 1 half life = 120 minutes / 6 half lives = 20 minutes

 

3.              The background radiation in a laboratory is 7 Bq. The count rate from a radioisotope is measured and it has a reading of 119 Bq. If the half life of the radioisotope is 10 minutes, what will be the reading 20 minutes later?

 

Initial count rate at detector = 119 Bq

But Background rate = 7 Bq

So activity of radioisotope = 119 – 7 = 112 Bq

 

1  è  ½  è  ¼

      1xhalf life    2xhalf life

    10mins   +  10mins = 20mins

112Bq  è  56Bq  è  28Bq = activity of radioisotope after 20 mins

 

But this doesn’t include the background rate!

Detector reading = 28Bq + 7Bq = 35Bq

 

4.              Potassium decays into argon.  The half life of potassium is 1.3 billion years.  A sample of rock from Mars is found to contain three argon atoms for every atom of potassium.  How old is the rock?

 

Proportion of K:       1  è  ½  è  ¼

Proportion of Ar:      0  è  ½  è  3/4   

                                                   1xhalf life    2xhalf life

So after 2 half lives there will be 3 times as many Ar atoms as K atoms

Age of rocks = 2 x half life = 2 x 1.3x10⁹ = 2.6 billion years