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physics Physics For High Schools (KS4)
 
Solved problems for the chapter:
 

Half-Life

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Radioactivity
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Detailed solution steps are available at:
 
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Example 1.

A radioactive isotope is placed near a detector. The readings on the detector are corrected for background radiation and recorded every hour. The table shows the corrected readings.




What is the half-life of the isotope?


  • between 0 and 1 hour

  • between 1 hour and 2 hours

  • between 2 hours and 3 hours

  • between 3 hours and 4 hours

    
Example 2.

The count rate due to a sample of a radioactive isotope is measured for 80 minutes.




What is the half-life of the isotope?


  • 20 minutes

  • 40 minutes

  • 60 minutes

  • 80 minutes

    
3.

A radioactive source produces a count rate on a detector of . After , the count rate has fallen to . Both count rates have been corrected for background radiation. What is the half-life of the source?






    
4.

A sample of a radioactive isotope emits 9600 -particles per second. After the rate of emission has fallen to 600 -particles per second. What is the half-life of this isotope?






    
5.

A sample of a radioactive isotope has a mass of . The half-life of the radioactive isotope is . Which graph shows the decay for this isotope?


    
6.

The graph shows the radioactive decay curve of a substance.




What is the half-life of this substance?






    
7.

A radioactive source has a half-life of . A detector near the source shows a reading of . Background radiation can be ignored. What is the reading on the detector later?






    
8.

A sample of a radioactive isotope has an initial rate of emission of and a half-life of . How long will it take for the rate of emission to fall to ?






    

9.

The graph shows how the count rate from a radioactive isotope changes with time.




What is the half-life of this isotope?






    
10.

The half-life of a sample of radioactive material is . How long will it take until only one-fourth of this sample remains undecayed?






    
11.

A radioactive substance has a half-life of . It has an initial rate of emission of . How long will it take for this rate of emission to fall to ?






    
12.

When a radioactive isotope is set up close to a counter, a count rate of is obtained. The table shows the count rate from the isotope over a three-year period.




What is the half-life of the isotope?


  • less than 1 year

  • more than 1 year but less than 2 years

  • more than 2 years but less than 3 years

  • more than 3 years

    
13.

A radioactive isotope has a half-life of 3 years. A sample gives a count rate of on a detector. Which calculation is used to predict the count rate after 12 years?






    
14.

A sample contains of a radioactive isotope. After the mass of the radioactive isotope in the sample falls to . What is the half-life of the radioactive isotope?






    
15.

The half-life for lead-202 is 52,500 years. A sample of lead-202 produces . How long will it take for the count rate to drop to ?


  • 105,000 years

  • 157,500 years

  • 210,000 years

  • 420,000 years

    
16.

In a laboratory, a detector of ionising radiation records an average background count rate of .




A radioactive source is now placed close to the detector. The count rate on the detector rises to .




What is the count rate due to radiation from the radioactive source?






    
17.

The graph shows how the decay rate of a radioactive source changes with time.




What will be the activity at 8 days?






    
18.

A student investigates how the radiation from a radioactive source changes with time. The table shows the results from the detector used by the student.




The experiment is repeated by many other students, who also measure the count rate every two minutes. The half-life of the source is known to be exactly 2.0 minutes. Why is the measured count rate always greater than half the previous value?


  • Radioactive emissions occur randomly with time.

  • The detector used is very close to the source.

  • There is background radiation present.

  • The radioactive source is decaying.

    

19.

A reading is taken every of the number of emissions per second from a radioactive source. The table shows the readings.




What is the half-life of the source?






    
20.

Bismuth-214 is radioactive. It has a half-life of 20 minutes. The count rate from a sample of bismuth-214 is . Predict the count rate from the sample after 60 minutes.