Timing the Invisible: Half Life Basics Physics Quiz

Concept: definition of half-life. Half-life measures how quickly decay happens. It is the time for the number of undecayed radioactive nuclei to drop to half its starting value.

Concept: isotope-specific decay. Each isotope has its own characteristic half-life. This value is determined by nuclear structure and does not depend on how the isotope is used.

Concept: halving rule. Half remain after one half-life. So 200 becomes about 100 because the sample is reduced by a factor of 2.

Concept: repeated halving. (1/2)^2 = 1/4. Each half-life multiplies the remaining amount by 1/2, so two half-lives gives (1/2) × (1/2).

Concept: half-life applies to amount of radioisotope. Mass halves after each half-life (for the radioactive part). If all 80 g is the radioisotope, after one half-life about 40 g remains undecayed.

Concept: half-life independence from sample size. Half-life does not depend on sample size. A bigger sample has more nuclei, but each nucleus still has the same decay probability per unit time.

Concept: counting half-lives. 10 days = 2 half-lives → (1/2)^2 = 1/4. Two halvings reduce the amount to one quarter of the original.

Concept: randomness at the single-nucleus level. You can’t predict exactly when one nucleus will decay. You can only talk about probabilities, which is why we use half-life for large numbers of nuclei.

Concept: statistics in large samples. Large numbers give stable averages. Even though individual decays are random, the overall fraction that decays in a given time becomes predictable.

Concept: repeated halving sequence. 1000 → 500 → 250 → 125. Three half-lives means three successive halvings, so the result is one eighth of the original.

Concept: fraction remaining after n half-lives. (1/2)^3 = 1/8. Each half-life multiplies the remaining fraction by 1/2, so after three you get 1/8.

Concept: exponential decay never hits exact zero. Decay is exponential and never reaches exactly zero. After each half-life, some nuclei still remain, so the amount keeps decreasing but does not abruptly finish.

Concept: interpreting half-life length. Shorter half-life means faster decay. A 1-day half-life means the sample halves every day, which is much quicker than years.

Concept: two half-lives gives one quarter. 1/4 requires 2 half-lives → 2×2=4 hours. Halving twice takes two half-life intervals.

Concept: core half-life facts. a, b, d are true. Half-life is isotope-specific, the amount halves each interval, and repeated halving produces an exponential decrease.

Concept: exponential decay tail. Exponential decay approaches zero gradually. The remaining amount can become extremely small, but it may not be exactly zero.

Concept: stability vs half-life. Long half-life means slow decay, not 'non-radioactive.' It can still be radioactive; it just changes more slowly over time.

Concept: applying two halvings. 64 → 32 → 16. Two half-lives means divide by 2 twice, giving one quarter of the starting amount.

Concept: half-life constancy. It’s constant for that isotope. The decay probability per unit time stays the same, so the halving time does not change.

Concept: half-life summary. Half-life is a decay time scale. It helps you predict how the amount (and activity) decreases in large samples over time.