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