4.2.2 Half-Life

• What is radioactive decay?

  Spontaneous emission of radiation
• Radioactive decay is the spontaneous and random process where unstable atomic nuclei transform into more stable nuclei by emitting radiation
• The half-life of a radioactive isotope is the time taken for half of the original nuclei to decay.
• Match the number of half-lives with the remaining quantity of nuclei:

  0 ↔️ 100%

  1 ↔️ 50%

  2 ↔️ 25%
• The half-life can be determined from decay data or graphs by measuring the time it takes for the initial activity to reduce to half
• What is the half-life of a substance if its activity halves in 5 seconds?

  5 seconds
• The half-life of a radioactive isotope is constant and unique for each isotope.
• Match the number of half-lives with the remaining quantity of nuclei:

  0 ↔️ 100%

  1 ↔️ 50%

  2 ↔️ 25%

  3 ↔️ 12.5%
• What should you look for in decay data tables to calculate half-life?

  Time for activity to halve
• The half-life can be calculated using the formula: T1/2 = (t2 - t1) / log₂(N1 / N2
• The half-life (T1/2) can be calculated using the formula: T1/2 = (t2 - t1) / log₂(N1 / N2)
• In the half-life formula, N1 and N2 represent the initial and final numbers of nuclei, respectively.
• Using the provided data, the calculated half-life is 5 seconds.
• The half-life of a radioactive substance can be determined from decay data, graphs, or formulas.
• Steps to interpret decay data tables

  1️⃣ Look for the time it takes for the activity to reduce by half

  2️⃣ Record the initial and halved values

  3️⃣ Note the corresponding times
• The decay constant (λ) is defined as the probability of a nucleus decaying per unit time.
• The half-life and decay constant are inversely proportional.
• What is the formula relating half-life (T1/2) and decay constant (λ)?

  $T_{1 / 2} =$$\frac{\ln 2}{\lambda}$
• In the half-life formula, ln 2 is approximately equal to 0.693.
• Match the real-world application with its use of half-life:

  Carbon Dating ↔️ Determines the age of ancient artifacts

  Medical Imaging ↔️ Diagnostic scans using Technetium-99m

  Cancer Treatment ↔️ Kills cancer cells with radiation
• Carbon dating helps historians understand the past by determining the age of ancient artifacts.