Physical

Isotope decay: practice problems

Work out the result for isotope decay. Every answer here is computed by the same tested calculator the rest of the site uses, so a solution can never drift away from the maths.

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Problem 1 Isotope decay

Work out the result for isotope decay.

  • Starting activity: 400
  • Time elapsed: 12.3
  • Half-life (same unit): 14.3
Show the answer and the working

After this time, 220.4 remains (55.09% of the start).

  1. Remaining fraction: exp(-0.6931 · 12.3 / 14.3) = 0.5509
  2. Remaining activity: A0 · fraction = 400 · 0.5509 = 220.4

Open this in the calculator to change the numbers.

Problem 2 Isotope decay

Work out the result for isotope decay.

  • Starting activity: 100
  • Time elapsed: 14.3
  • Half-life (same unit): 14.3
Show the answer and the working

After this time, 50 remains (50% of the start).

  1. Remaining fraction: exp(-0.6931 · 14.3 / 14.3) = 0.5
  2. Remaining activity: A0 · fraction = 100 · 0.5 = 50

Open this in the calculator to change the numbers.

Problem 3 Isotope decay

Work out the result for isotope decay.

  • Starting activity: 400
  • Time elapsed: 15.3
  • Half-life (same unit): 14.3
Show the answer and the working

After this time, 190.5 remains (47.63% of the start).

  1. Remaining fraction: exp(-0.6931 · 15.3 / 14.3) = 0.4763
  2. Remaining activity: A0 · fraction = 400 · 0.4763 = 190.5

Open this in the calculator to change the numbers.

Problem 4 Isotope decay

Work out the result for isotope decay.

  • Starting activity: 500
  • Time elapsed: 16.3
  • Half-life (same unit): 14.3
Show the answer and the working

After this time, 226.9 remains (45.38% of the start).

  1. Remaining fraction: exp(-0.6931 · 16.3 / 14.3) = 0.4538
  2. Remaining activity: A0 · fraction = 500 · 0.4538 = 226.9

Open this in the calculator to change the numbers.

Problem 5 Isotope decay

Work out the result for isotope decay.

  • Starting activity: 300
  • Time elapsed: 15.3
  • Half-life (same unit): 14.3
Show the answer and the working

After this time, 142.9 remains (47.63% of the start).

  1. Remaining fraction: exp(-0.6931 · 15.3 / 14.3) = 0.4763
  2. Remaining activity: A0 · fraction = 300 · 0.4763 = 142.9

Open this in the calculator to change the numbers.

Problem 6 Isotope decay

Work out the result for isotope decay.

  • Starting activity: 100
  • Time elapsed: 17.3
  • Half-life (same unit): 14.3
Show the answer and the working

After this time, 43.23 remains (43.23% of the start).

  1. Remaining fraction: exp(-0.6931 · 17.3 / 14.3) = 0.4323
  2. Remaining activity: A0 · fraction = 100 · 0.4323 = 43.23

Open this in the calculator to change the numbers.

Problem 7 Isotope decay

Work out the result for isotope decay.

  • Starting activity: 100
  • Time elapsed: 14.8
  • Half-life (same unit): 14.3
Show the answer and the working

After this time, 48.8 remains (48.8% of the start).

  1. Remaining fraction: exp(-0.6931 · 14.8 / 14.3) = 0.488
  2. Remaining activity: A0 · fraction = 100 · 0.488 = 48.8

Open this in the calculator to change the numbers.

Problem 8 Isotope decay

Work out the result for isotope decay.

  • Starting activity: 100
  • Time elapsed: 12.3
  • Half-life (same unit): 14.3
Show the answer and the working

After this time, 55.09 remains (55.09% of the start).

  1. Remaining fraction: exp(-0.6931 · 12.3 / 14.3) = 0.5509
  2. Remaining activity: A0 · fraction = 100 · 0.5509 = 55.09

Open this in the calculator to change the numbers.

Problem 9 Isotope decay

Work out the result for isotope decay.

  • Starting activity: 150
  • Time elapsed: 14.3
  • Half-life (same unit): 14.3
Show the answer and the working

After this time, 75 remains (50% of the start).

  1. Remaining fraction: exp(-0.6931 · 14.3 / 14.3) = 0.5
  2. Remaining activity: A0 · fraction = 150 · 0.5 = 75

Open this in the calculator to change the numbers.

Problem 10 Isotope decay

Work out the result for isotope decay.

  • Starting activity: 300
  • Time elapsed: 14.3
  • Half-life (same unit): 14.3
Show the answer and the working

After this time, 150 remains (50% of the start).

  1. Remaining fraction: exp(-0.6931 · 14.3 / 14.3) = 0.5
  2. Remaining activity: A0 · fraction = 300 · 0.5 = 150

Open this in the calculator to change the numbers.

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Open the Isotope decay calculator