4.2.3 Half-Lives and the Random Nature of Radioactive Decay

In this lesson, we will explore the concept of half-lifeThe time it takes for half the atoms of a radioactive substance to decay; for carbon-14, this is approximately 5,700 years. and how it relates to the random nature of radioactive decay.

Random Nature of Radioactive Decay

Radioactive decay is a random process. It cannot be predicted exactly when an individual radioactive nucleusA membrane-bound organelle in eukaryotic cells that contains DNA. will decay.

The decay of a radioactive nucleus is not influenced by external factors such as temperature, pressure, or chemical composition. Each nucleus has an equal probability of decaying at any given moment.

Half-Life

The half-life of a radioactive isotopeVariants of a chemical element with the same number of protons but different numbers of neutrons; some are stable, others (like carbon-14) are radioactive. is the time it takes for the number of nuclei of the isotope in a sample to halve, or the time it takes for the count rate (or activity) from a sample containing the isotope to fall to half its initial level.

• Constant Fraction: The half-life is a characteristic property of each radioactive isotope. Regardless of the size of the sample, half of the radioactive nuclei will decay within one half-life.
• Different Half-Lives: Different radioactive isotopes have different half-lives. Some may have short half-lives, while others may have long half-lives.

Conceptual Understanding

Relationship to Random Nature: The concept of half-life is related to the random nature of radioactive decay. Since decay is random, we cannot predict exactly which nuclei will decay and when. However, over a large number of nuclei, the decay follows a predictable pattern expressed by the half-life.

Determining Half-Life

To determine the half-life of a radioactive isotope, you can utilise various types of information provided. This may include:

• Initial Count Rate: The count rate at the beginning of the observation period is measured. The count rate represents the number of radioactive decays recorded per unit of time.
• Count Rate after a Certain Time: The count rate is measured again after a specific time interval has passed. By comparing the count rate at the beginning and after the given time, students can determine how much the count rate has decreased.
• Number of Remaining Nuclei: Instead of measuring the count rate, students may be given the number of remaining radioactive nuclei in a sample after a certain time.

Using this given information, you can analyse the decay process and determine the time it takes for the number of nuclei or count rate to reduce by half. This time interval represents the half-life of the radioactive isotope.

Calculating Net Decline

Calculating the net decline involves determining the remaining fraction of radioactive nuclei after a given number of half-lives.

• Determining the Number of Half-Lives: The given information may specify the number of half-lives that have elapsed. Each half-life corresponds to a 50% reduction in the number of radioactive nuclei or count rate.
• Calculating the Remaining Fraction: To calculate the net decline, determine the fraction of remaining radioactive nuclei. This can be done by dividing the number of remaining nuclei by the initial number of nuclei or by dividing the count rate after a certain time by the initial count rate.
• Expressing as a Ratio: The net decline is typically expressed as a ratio, such as the remaining fraction of nuclei compared to the initial fraction or the remaining count rate compared to the initial count rate.

Conclusion

Radioactive decay is a random process that cannot be predicted exactly for individual nuclei. It is not influenced by external factors, and each nucleus has an equal probability of decaying at any moment. The half-life of a radioactive isotope is a characteristic property, and different isotopes have different half-lives. The concept of half-life is related to the random nature of decay, as it provides a predictable pattern for a large number of nuclei. To determine the half-life, measurements of initial count rates, count rates after a certain time, or the number of remaining nuclei can be utilised.