Free Half-life and Rate of Decay MCQs with Answers

1. The half life of a radioactive sample is the time in which

• A. the whole sample decays
• B. half the undecayed nuclei present decay
• C. the activity becomes zero
• D. the mass of the sample halves

Explanation: Decay is a random process with a constant probability per nucleus per unit time, so a fixed fraction rather than a fixed number decays in each interval, which is what makes the half life constant. After two half lives one quarter remains, after three one eighth, and the count never quite reaches zero. The mass of the sample barely changes, since the daughter nuclei are almost as heavy.

2. A radioactive sample has a half life of 8 days. The fraction remaining undecayed after 24 days is

• A. one half
• B. one quarter
• C. one eighth
• D. one sixteenth

Explanation: Twenty four days is three half lives, so the sample is halved three times, leaving one half multiplied by one half multiplied by one half, which is one eighth. A common error is to divide 24 by 8 and answer one third, which misunderstands the exponential nature of decay. Iodine 131, used in thyroid treatment, has almost exactly this half life.

3. The activity of a radioactive source is measured in

• A. becquerel
• B. gray
• C. sievert
• D. coulomb

Explanation: One becquerel is one disintegration per second, so it measures how fast the source is decaying. The gray measures absorbed dose in joules per kilogram and the sievert measures the biologically weighted equivalent dose, which is what radiation protection limits are quoted in. Keeping these three units apart is a common examination point.

4. Carbon dating is possible because

• A. carbon 14 is stable
• B. living things take in carbon 14 while alive, and it then decays with a known half life after death
• C. all carbon is radioactive
• D. carbon 14 is produced in the body

Explanation: While an organism lives it exchanges carbon with its surroundings and holds the atmospheric ratio of carbon 14 to carbon 12, but after death intake stops and the carbon 14 decays with a half life of about 5730 years. Measuring the remaining ratio therefore gives the time since death. The method is useful up to roughly 50,000 years, after which too little carbon 14 remains.

5. After 3 half-lives, the remaining fraction of a radioactive sample is:

• A. 1/2
• B. 1/4
• C. 1/8
• D. 1/16

Explanation: Each half life halves the number of undecayed nuclei, so three of them give a half multiplied by a half multiplied by a half, which is one eighth. Decay is exponential, so the fractions multiply rather than the half lives adding in any simple way. After four half lives one sixteenth would remain.

6. The time in which half of the given number of radioactive nuclei decay is known as

• A. 1/2 life of radioactive element
• B. 2/3 life of radioactive element
• C. 1/4 life of radioactive element
• D. 2/5 life of radioactive element

Explanation: The half life is the interval in which half the undecayed nuclei present decay, and because decay is random with a constant probability per nucleus, that interval stays the same however much material remains. Carbon 14 has a half life of about 5730 years and iodine 131 about 8 days. The quantity is a property of the nuclide and cannot be altered by temperature or pressure.