Worksheet: Biological Half-life

In this worksheet, we will practice calculating the effective half-life of a substance from its physical half-life and its biological half-life.

Q1:

A radioisotope has a physical decay constant of 3 . 9 0 × 1 0 s−1 and a biological decay constant of 1 . 7 6 × 1 0 s−1. What is the effective decay constant of the radioisotope? Give your answer to 3 significant figures.

  • A 2 . 1 5 × 1 0 s−1
  • B 3 . 1 9 × 1 0 s−1
  • C 1 . 3 7 × 1 0 s−1
  • D 5 . 0 1 × 1 0 s−1
  • E 6 . 8 7 × 1 0 s−1

Q2:

A radioisotope has a physical half-life of 45.2 days and a biological half-life of 15.0 days. What is the effective half-life of the radioisotope? Give your answer to 3 significant figures.

Q3:

Polonium-210 has a physical half-life of 138 days and a biological half-life of 40 days. What is the effective half-life of polonium-210? Give your answer to 3 significant figures.

Q4:

If it is in the blood, lead-209 has a physical decay constant of 5 . 9 2 × 1 0 s−1 and a biological decay constant of 2 . 6 7 × 1 0 s−1. What is the effective decay constant for lead? Give your answer to 3 significant figures.

  • A 1 . 5 8 × 1 0 s−1
  • B 2 . 6 6 × 1 0 s−1
  • C 2 . 7 8 × 1 0 s−1
  • D 5 . 8 9 × 1 0 s−1
  • E 5 . 9 5 × 1 0 s−1

Q5:

Which of the following formulas correctly shows how the effective decay constant of a substance relates to its physical decay constant and its biological decay constant?

  • A 𝜆 = 𝜆 × 𝜆
  • B 𝜆 = 𝜆 𝜆
  • C 𝜆 = 𝜆 + 𝜆
  • D 1 𝜆 = 1 𝜆 + 1 𝜆
  • E 1 𝜆 = 1 𝜆 1 𝜆

Q6:

The table shows the physical and biological half-lives for four radioisotopes.

Isotope Physical Half-life (Days) Biological Half-life (Days)
A 20.2 30.5
B 34.8 35.6
C 89.0 29.8
D 12.5 40.1

Which radioisotope has the shortest effective half-life?

  • AC
  • BA
  • CD
  • DB

Q7:

Which of the following formulas correctly shows how the effective half-life of a substance relates to its physical and biological half-lives?

  • A 1 𝑡 = 1 𝑡 + 1 𝑡
  • B 𝑡 = 𝑡 × 𝑡
  • C 1 𝑡 = 1 𝑡 × 1 𝑡
  • D 1 𝑡 = 1 𝑡 1 𝑡
  • E 𝑡 = 𝑡 + 𝑡

Q8:

Which of the following is the correct definition of effective half-life?

  • AThe effective half-life of a substance is the amount of time it takes for the amount of that substance within the body to reduce to zero when both physical and biological processes act to reduce the amount of the substance within the body.
  • BThe effective half-life of a substance is the amount of time it takes for the amount of that substance within the body to reduce by half when both physical and biological processes act to reduce the amount of the substance within the body.
  • CThe effective half-life of a substance is the amount of time it takes for the amount of that substance within the body to reduce by half when only biological processes act to reduce the amount of the substance within the body.
  • DThe effective half-life of a substance is the amount of time it takes for the amount of that substance within the body to reduce to zero when only biological processes act to reduce the amount of the substance within the body.

Q9:

Which of the following is the correct definition of biological half-life?

  • AThe biological half-life of a substance is the amount of time it takes for the amount of that substance within the body to reduce to zero by radioactive decay.
  • BThe biological half-life of a substance is the amount of time it takes for biological processes to remove half of that substance from the body.
  • CThe biological half-life of a substance is the amount of time it takes for biological processes to remove all of that substance from the body.
  • DThe biological half-life of a substance is the amount of time it takes for the amount of that substance within the body to reduce by half by radioactive decay.

Q10:

If a radioisotope has a physical half-life of 2 days and a biological half-life of 2 days, will its effective half-life be greater or less than 2 days?

  • ALess than 2 days
  • BGreater than 2 days

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