Half-life of isotopes MCQs With Answer

Understanding the half-life of isotopes is vital for B. Pharm students specializing in radiopharmacy, pharmacokinetics, and nuclear medicine. This clear, SEO-friendly introduction covers core concepts: radioactive decay, decay constant, mathematical relations for activity, effective and biological half-life, and practical unit conversions (becquerel, curie). It highlights important clinical radioisotopes such as technetium-99m, fluorine-18, and iodine-131, and explains secular and transient equilibrium, parent–daughter dynamics, and dose calculation principles. Emphasis on worked examples sharpens quantitative skills needed for safe dosing, storage, and regulatory compliance. Answers include brief explanations to strengthen conceptual understanding and exam readiness. Now let’s test your knowledge with 50 MCQs on this topic.

Q1. What is the definition of the half-life of an isotope?

• The time required for the activity to reduce by 25%
• The time required for half the original number of nuclei to decay
• The time required for activity to become zero
• The average time between successive decays of a nucleus

Correct Answer: The time required for half the original number of nuclei to decay

Q2. Which formula correctly relates half-life (t1/2) and decay constant (λ)?

• t1/2 = λ / ln2
• t1/2 = ln2 / λ
• t1/2 = e^(λ)
• t1/2 = 1 / (λ ln2)

Correct Answer: t1/2 = ln2 / λ

Q3. Which equation gives activity A at time t for an initial activity A0?

• A = A0 (1 + λt)
• A = A0 e^(λt)
• A = A0 e^(-λt)
• A = A0 / (1 + λt)

Correct Answer: A = A0 e^(-λt)

Q4. What is the mean life (average lifetime) τ of a radionuclide in terms of λ?

• τ = ln2 / λ
• τ = 1 / (λ ln2)
• τ = 1 / λ
• τ = λ

Correct Answer: τ = 1 / λ

Q5. After three half-lives, what fraction of the original nuclei remains?

• 1/2
• 1/3
• 1/8
• 1/16

Correct Answer: 1/8

Q6. Technetium-99m has an approximate half-life of 6 hours. What fraction remains after 12 hours?

• 1/4
• 1/2
• 1/8
• 3/4

Correct Answer: 1/4

Q7. If a sample has activity 800 Bq and λ = 0.1 h⁻¹, what is activity after 5 hours? (Use A=A0 e^-λt)

• ~485 Bq
• ~300 Bq
• ~600 Bq
• ~200 Bq

Correct Answer: ~485 Bq

Q8. Which unit is the SI unit for radioactivity?

• Curie (Ci)
• Becquerel (Bq)
• Gray (Gy)
• Sievert (Sv)

Correct Answer: Becquerel (Bq)

Q9. How many becquerels equal 1 curie (approx)?

• 3.7 × 10⁸ Bq
• 3.7 × 10¹⁰ Bq
• 3.7 × 10⁶ Bq
• 3.7 × 10¹² Bq

Correct Answer: 3.7 × 10¹⁰ Bq

Q10. Which isotope commonly used in PET has a half-life of about 110 minutes?

• Iodine-131
• Technetium-99m
• Fluorine-18
• Carbon-14

Correct Answer: Fluorine-18

Q11. What is secular equilibrium between parent and daughter nuclide?

• Parent and daughter have equal half-lives
• Daughter builds up to a constant activity equal to parent when parent half-life ≫ daughter half-life
• Parent decays instantly to daughter
• Neither decays

Correct Answer: Daughter builds up to a constant activity equal to parent when parent half-life ≫ daughter half-life

Q12. In transient equilibrium which statement is true?

• Parent half-life ≪ daughter half-life
• Parent and daughter have identical half-lives
• Parent half-life is a few times longer than daughter half-life, producing a temporary equilibrium
• Daughter never reaches any equilibrium

Correct Answer: Parent half-life is a few times longer than daughter half-life, producing a temporary equilibrium

Q13. Effective half-life (Teff) combines physical (Tphys) and biological (Tbio) half-lives. Which relation is correct?

• 1/Teff = 1/Tphys + 1/Tbio
• Teff = Tphys + Tbio
• Teff = (Tphys × Tbio) / (Tphys – Tbio)
• Teff = Tphys / Tbio

Correct Answer: 1/Teff = 1/Tphys + 1/Tbio

Q14. If physical half-life = 8 days and biological half-life = 16 days, what is effective half-life?

• ~5.3 days
• ~10.7 days
• ~24 days
• ~4 days

Correct Answer: ~5.3 days

Q15. Which isotope is commonly used for thyroid therapy with a half-life of ~8 days?

• Iodine-131
• Technetium-99m
• Fluorine-18
• Phosphorus-32

Correct Answer: Iodine-131

Q16. Specific activity refers to:

• Activity per mass of sample
• Total mass of sample
• Number of half-lives elapsed
• Activity per volume only

Correct Answer: Activity per mass of sample

Q17. Which isotope is widely used in diagnostic imaging with very short half-life (~6 hours)?

• Carbon-14
• Technetium-99m
• Cesium-137
• Uranium-238

Correct Answer: Technetium-99m

Q18. If A0 = 1000 Bq and half-life = 2 hours, what is activity after 6 hours?

• 500 Bq
• 250 Bq
• 125 Bq
• 750 Bq

Correct Answer: 125 Bq

Q19. What happens to decay constant λ when half-life increases?

• λ increases
• λ decreases
• λ remains unchanged
• λ oscillates

Correct Answer: λ decreases

Q20. Which of these isotopes has a very long half-life suitable for dating archaeological samples?

• Fluorine-18
• Carbon-14
• Technetium-99m
• Phosphorus-32

Correct Answer: Carbon-14

Q21. How many half-lives must pass for activity to drop to ~3.125% of original?

• 3 half-lives
• 5 half-lives
• 7 half-lives
• 10 half-lives

Correct Answer: 5 half-lives

Q22. Which term describes branching where radionuclide decays via more than one mode?

• Secular equilibrium
• Branching ratio
• Transient decay
• Isomeric transition

Correct Answer: Branching ratio

Q23. In radioactivity decay counting, shorter half-life leads to which measurement challenge?

• Lower statistical uncertainty
• Higher statistical uncertainty if counts are low
• No change in counting statistics
• Impossible to measure

Correct Answer: Higher statistical uncertainty if counts are low

Q24. Which is true for a daughter nuclide in secular equilibrium?

• Daughter activity << parent activity always
• Daughter activity ≈ parent activity after buildup
• Daughter activity never increases
• Daughter decays before being formed

Correct Answer: Daughter activity ≈ parent activity after buildup

Q25. How is dose rate from a point source related to activity if shielding and distance are constant?

• Directly proportional to activity
• Inverse proportional to activity
• Independent of activity
• Proportional to square of activity

Correct Answer: Directly proportional to activity

Q26. Which radionuclide is commonly used for bone marrow and cancer therapy with β-emission and half-life ~14 days?

• Phosphorus-32
• Technetium-99m
• Fluorine-18
• Iodine-131

Correct Answer: Phosphorus-32

Q27. What is the activity ratio A/A0 after one mean life τ?

• 1/e (~0.3679)
• 1/2
• ln2
• e

Correct Answer: 1/e (~0.3679)

Q28. When planning radionuclide dosing, why is knowledge of half-life critical?

• To determine flavor of radiopharmaceutical
• To calculate shelf life, optimal imaging time, and patient dose
• To make isotope heavier
• To convert activity to mass directly

Correct Answer: To calculate shelf life, optimal imaging time, and patient dose

Q29. If a parent has half-life 5 days and daughter 1 day, what equilibrium type likely occurs?

• Secular equilibrium
• Transient equilibrium
• No equilibrium possible
• Kinetic equilibrium

Correct Answer: Secular equilibrium

Q30. Which quantity decreases exponentially with time for a radioactive sample?

• Number of undecayed nuclei
• Half-life
• Decay constant
• Specific activity per mass if mass changes

Correct Answer: Number of undecayed nuclei

Q31. How would you calculate the age of an archaeological sample using C-14 if remaining fraction is 0.25 and t1/2 = 5730 years?

• ~2865 years
• ~5730 years
• ~11460 years
• ~17190 years

Correct Answer: ~11460 years

Q32. What is branching ratio 0.8 for a decay mode?

• 80% of decays follow that mode
• 0.8 decays per second
• 80 decays total
• 10% of decays follow that mode

Correct Answer: 80% of decays follow that mode

Q33. Which of the following affects the effective half-life of a radiopharmaceutical in a patient?

• Only chemical form
• Only physical half-life
• Both physical half-life and biological elimination
• Only ambient temperature

Correct Answer: Both physical half-life and biological elimination

Q34. If activity halves every 4 hours, what is λ (per hour)? (t1/2=4)

• 0.1733 h⁻¹
• 0.25 h⁻¹
• ln2 h⁻¹
• 4 h⁻¹

Correct Answer: 0.1733 h⁻¹

Q35. Which practice improves radiopharmacy safety regarding half-life?

• Ignoring decay when storing radionuclides
• Calculating decay to determine safe storage and disposal timing
• Mixing isotopes to extend half-life
• Storing all waste indefinitely

Correct Answer: Calculating decay to determine safe storage and disposal timing

Q36. What is the activity remaining after 1.5 half-lives?

• ~35.35% of original
• ~50% of original
• ~25% of original
• ~75% of original

Correct Answer: ~35.35% of original

Q37. Which statement about long-lived isotopes like Cs-137 is correct for pharmacy waste?

• They require brief storage only
• They may need long-term containment due to long half-life
• They decay completely within days
• They are safe to release immediately

Correct Answer: They may need long-term containment due to long half-life

Q38. How does chemical binding of a radionuclide in vivo affect its biological half-life?

• Binding may increase retention and lengthen biological half-life
• Binding always shortens biological half-life
• Chemical binding only affects physical half-life
• No effect at all

Correct Answer: Binding may increase retention and lengthen biological half-life

Q39. Which formula gives remaining fraction after time t in terms of half-life?

• (1/2)^(t/t1/2)
• t × t1/2
• ln(2) × t
• t1/2 / t

Correct Answer: (1/2)^(t/t1/2)

Q40. If a diagnostic dose is prepared at 08:00 and imaging is optimal at 4 hours considering isotope half-life, which concept was used?

• Secular equilibrium
• Decay curve and biological distribution timing
• Specific activity only
• Branching ratio

Correct Answer: Decay curve and biological distribution timing

Q41. How does temperature typically affect nuclear half-life?

• Temperature dramatically changes nuclear half-life
• Temperature generally has negligible effect on nuclear half-life
• Higher temperature doubles half-life
• Lower temperature stops decay

Correct Answer: Temperature generally has negligible effect on nuclear half-life

Q42. Which isotope is commonly used in external beam radiotherapy and has a half-life of several years?

• Cobalt-60
• Technetium-99m
• Fluorine-18
• Carbon-14

Correct Answer: Cobalt-60

Q43. For a radionuclide with half-life 30 days, what percentage remains after 60 days?

• 25%
• 50%
• 75%
• 12.5%

Correct Answer: 25%

Q44. Which instrument measures activity by detecting decays?

• Spectrophotometer
• Geiger-Müller counter
• pH meter
• Thermometer

Correct Answer: Geiger-Müller counter

Q45. If A0 = 5000 Bq and after 24 hours A = 1250 Bq, what is the number of half-lives elapsed?

• 1 half-life
• 2 half-lives
• 3 half-lives
• 4 half-lives

Correct Answer: 2 half-lives

Q46. Which parameter is most useful to estimate radionuclide clearance from a biological compartment?

• Physical half-life only
• Biological half-life
• Atomic number
• Specific gravity

Correct Answer: Biological half-life

Q47. What is the main reason short half-life isotopes are preferred for diagnostic imaging?

• They produce permanent radioactivity
• They minimize radiation dose to patient while allowing imaging
• They are cheaper always
• They do not emit radiation

Correct Answer: They minimize radiation dose to patient while allowing imaging

Q48. When calculating parent-daughter activities over time, which differential equation concept is used?

• Newton’s laws
• Coupled first-order decay equations
• Maxwell’s equations
• Ideal gas law

Correct Answer: Coupled first-order decay equations

Q49. Which radionuclide property influences choice for therapeutic use?

• Only color
• Type and energy of emissions and half-life suitable for dose delivery
• Odor
• Boiling point

Correct Answer: Type and energy of emissions and half-life suitable for dose delivery

Q50. For regulatory decay storage, a rule-of-thumb is to store waste for how many half-lives to reduce activity substantially?

• About 1 half-life
• About 10 half-lives
• About 2 half-lives
• About 100 half-lives

Correct Answer: About 10 half-lives