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Physics · Grades 9–12

Expected amount after half-lives

This predicts the expected remaining amount for a large ensemble; individual decays are random.

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Rule and assumptions

This predicts the expected remaining amount for a large ensemble; individual decays are random.

N = N₀(½)ⁿ

Worked examples

A model sample begins with 90000 undecayed nuclei. Half-life is 18 h. Find the expected number still undecayed after 18 h. Round to 3 decimal places if needed.

N = N₀(½)ⁿ 18/18 = 1; 90000/2^1 = 45000

45000

A model sample begins with 1152000 undecayed nuclei. Half-life is 20 h. Find the expected number still undecayed after 120 h. Round to 3 decimal places if needed.

N = N₀(½)ⁿ 120/20 = 6; 1152000/2^6 = 18000

18000

Try two questions

  1. A model sample begins with 88000 undecayed nuclei. Half-life is 11 h. Find the expected number still undecayed after 22 h. Round to 3 decimal places if needed.

  2. A model sample begins with 864000 undecayed nuclei. Half-life is 22 h. Find the expected number still undecayed after 110 h. Round to 3 decimal places if needed.

Answers and reasoning

Answers and marking notes
  1. 22000

    N = N₀(½)ⁿ 22/11 = 2; 88000/2^2 = 22000

  2. 27000

    N = N₀(½)ⁿ 110/22 = 5; 864000/2^5 = 27000

Further reading and review references

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Learning preview · independent educational and translation review required. Suggested grades are not official curriculum alignment.