The Decay Constant and the Exponential Decay Law · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

The clockwork inside random decay

Science · Matter & Materials · ages 17-18
Name ______________________   Date ____________

  1. Each nucleus decays at random, but averages over trillions are rock steady.

    Circle one:   True   False

  2. What does the decay constant lambda describe?

    • The total decays in the sample
    • The age of the sample
    • Chance per nucleus per second

  3. A nuclide has a very short half-life. What does that say about its lambda?

    • Lambda is small
    • Lambda is large
    • Lambda is zero

  4. You plot the natural log of the count against time. What is the slope of the straight line?

    • Minus lambda
    • Plus lambda
    • Lambda squared

  5. A sample of 8000 nuclei passes through 3 half-lives. How many nuclei are left?

    Answer: ______________

  6. A nuclide has a half-life of 6 s. Use lambda = 0.693 / half-life. Give lambda per second.

    Answer: ______________

  7. Sample B holds twice the nuclei of sample A, same nuclide. How do their decay constants compare?

    • B has double the lambda
    • Both share the same lambda
    • B has half the lambda

  8. Leo says after two half-lives nothing of a sample remains. What is true?

    • Nothing remains
    • Half remains
    • A quarter remains
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Answer key

For grown-ups. Fold this page away before handing over the rest.

The clockwork inside random decay W1-mt_VIydSAys1W-s1

  1. True · Single throws are chance, yet huge numbers smooth into a fixed curve.
  2. Chance per nucleus per second · Lambda is the per-nucleus chance each second, shared by the whole kind.
  3. Lambda is large · Lambda equals 0.693 over half-life, so a tiny bottom gives a large lambda.
  4. Minus lambda · The log plot straightens the curve, and its slope reads minus lambda.
  5. 1000 · Three halvings leave one eighth: 8000 over 8 is 1000.
  6. 0.1155 · Divide 0.693 by 6 to get 0.1155 per second.
  7. Both share the same lambda · Lambda is a per-nucleus chance, so sample size never changes it.
  8. A quarter remains · Each half-life halves the remainder, so two leave one half squared: a quarter.
Worksheet · LightMySky