4.2.2 Half-Life

• Radioactive decay is the spontaneous breakdown of unstable atomic nuclei
• The half-life of a radioactive isotope is the time it takes for all the nuclei in a sample to decay.

  False
• What is the half-life of a radioactive isotope?

  Time for half decay
• T_{1 / 2}</latex> represents the half-life
• The half-life of a radioactive isotope is constant for each specific isotope.
• An isotope has an initial amount of 800 nuclei and a half-life of 10 years. After 20 years, how many nuclei will remain?

  200
• Match the variable with its description:

  N ↔️ Remaining nuclei

  N_{0} ↔️ Initial nuclei

  T_{1 / 2} ↔️ Half-life

  t ↔️ Time elapsed
• Starting with 1000 nuclei of an isotope with a half-life of 10 years, how many nuclei remain after 20 years?

  250
• A shorter half-life indicates a slower decay rate.

  False
• The decay rate measures the speed of radioactive decay
• What is the rate of radioactive decay dependent on?

  Half-life
• If Isotope A has a half-life of 5 years and Isotope B has a half-life of 50 years, Isotope A decays ten times faster
• The rate of radioactive decay is directly proportional to the half-life of an isotope.

  False
• What type of relationship exists between half-life and decay rate?

  Inverse
• Radiocarbon dating is used in archaeology to determine the age of organic artifacts
• What is the age of a bone sample if it contains25% of its original C-14 and the half-life of C-14 is 5730 years?

  11460 years
• Match the term with its definition:

  Radioactive Decay ↔️ Spontaneous breakdown of unstable nuclei

  Alpha Particle ↔️ Released during radioactive decay
• What is the half-life of a radioactive isotope?

  Time for half decay
• In the half-life equation, $T_{1 / 2}$ represents the half-life
• If an isotope has a half-life of 10 years, after 20 years, one-fourth of the original nuclei will remain.
• What is the decay equation used to calculate half-life?

  N = N_{0}(\frac{1}{2})^{\frac{t}{T_{1 / 2}}}</latex>
• In the decay equation, $T_{1 / 2}$ represents the half-life
• An isotope has an initial amount of 800 nuclei and a half-life of 10 years. How many nuclei will remain after 20 years?

  200
• Match the field with its application of half-life:

  Archaeology ↔️ Radiocarbon dating

  Medicine ↔️ Nuclear medicine

  Industry ↔️ Process monitoring
• What is the half-life of carbon-14, which is used in archaeology?

  5730 years