What is the length of time required for half of the radioactive atoms in a sample to decay called?

What is the length of time required for half of the radioactive atoms in a sample to decay called?

• A. Decay Constant
• B. Fusion energy production
• C. Half-life
• D. Critical mass

Answer: (C)

Half-life is the time required for half of the radioactive atoms in a sample to decay. It comes from the exponential decay law, N(t) = N0 e^{-λt}, where λ is the decay constant. The half-life t1/2 is the time when N(t1/2) = N0/2, giving t1/2 = ln 2 / λ ≈ 0.693/λ. This means the amount remaining halves after each half-life, a fundamental, isotope-specific time scale of decay. The decay constant describes how fast the process happens, but the half-life is the actual interval over which half the atoms decay. The other options refer to different nuclear concepts: fusion energy production is about combining nuclei, not decay timing, and critical mass concerns sustaining a chain reaction, not decay intervals.

Half-life is the time required for half of the radioactive atoms in a sample to decay. It comes from the exponential decay law, N(t) = N0 e^{-λt}, where λ is the decay constant. The half-life t1/2 is the time when N(t1/2) = N0/2, giving t1/2 = ln 2 / λ ≈ 0.693/λ. This means the amount remaining halves after each half-life, a fundamental, isotope-specific time scale of decay. The decay constant describes how fast the process happens, but the half-life is the actual interval over which half the atoms decay. The other options refer to different nuclear concepts: fusion energy production is about combining nuclei, not decay timing, and critical mass concerns sustaining a chain reaction, not decay intervals.