📝 Radiometric dating and half life (13 MCQs)

📖 From Campbell Biology • 2. The Chemistry of Life • 13 questions available

←Previous Topic:Radioactive tracers in biology and medicine📝 Radiometric dating and half lifeElectron energy levels shells:Next Topic→

What is Radiometric dating and half life?

Definition:
Radiometric dating is a technique used to determine the age of rocks, fossils, and archeological artifacts by measuring the decay of radioactive isotopes, relying on the half-life, which is the time required for half of a radioactive isotope's atoms to decay into a stable daughter product, and this method provides absolute dates and is fundamental to geology and paleontology.

Working:
Radiometric dating works by measuring the ratio of parent isotope to daughter isotope in a sample and knowing the half-life ( $t_{1/2}$ ), using the equation $t = \frac{1}{\lambda} \ln\left(\frac{N_0}{N}\right)$ , where $\lambda = \frac{0.693}{t_{1/2}}$ ; for example, carbon-14 dating measures $^{14}C$ to $^{14}N$ decay, with a half-life of 5730 years, and is used for organic materials up to about 50,000 years; by comparing the ratio to the initial amount, the age is calculated, and this method is calibrated with other dating techniques to ensure accuracy.

Example:
A simple example is dating a wooden artifact: if it has 25% of its original carbon-14, then it has undergone two half-lives, so it is $2 \times 5730 = 11,460$ years old; another example is dating rocks using uranium-238 ( $t_{1/2} = 4.5$ billion years) to date the Earth, providing evidence for the age of the Earth at about 4.5 billion years.

Reason:
Radiometric dating is essential for understanding the age of the Earth, the timing of evolutionary events, and the history of climate change, and it has profound implications for geology, paleontology, and archaeology.

Easy

Medium

Hard

📝 All Radiometric dating and half life MCQs

Q1. A radioactive isotope has a half-life of 5,000 years. If a mineral originally contained 80 mg of the isotope and now contains 20 mg, approximately how old is the mineral?

A.5,000 years

B.10,000 years ✅

C.15,000 years

D.20,000 years

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: After one half-life, 80 mg becomes 40 mg. After a second, it becomes 20 mg. Because two half-lives have elapsed and each lasts 5,000 years, the estimated age is $2 \times 5,000 = 10,000$ years.

Q2. Which statement best explains why the presence of radioactive isotopes can be used to estimate the age of a mineral?

A.Radioactive isotopes decay at a predictable statistical rate, allowing parent-to-daughter ratios to provide an elapsed-time estimate ✅

B.Radioactive isotopes always decay completely after one half-life

C.The amount of daughter isotope directly equals the mineral's age

D.Radioactive isotopes stop decaying when minerals crystallize

💡 Difficulty: medium | ✅ Correct: A

📖 Explanation: Radiometric dating works because radioactive decay follows a predictable probability distribution characterized by a half-life. If the system remains sufficiently closed, measuring parent and daughter quantities allows scientists to infer how much decay has occurred and estimate elapsed time.

Q3. Two minerals crystallized at the same time. Mineral X contains 25% of its original radioactive parent isotope, while Mineral Y contains 50%. Assuming both minerals use the same isotope and remained closed, what can be concluded?

A.X is younger because it contains less daughter isotope

B.Y is older because it contains more parent isotope

C.X is older because more radioactive parent isotope has decayed ✅

D.Both must have identical ages regardless of isotope concentration

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: A remaining fraction of 50% corresponds to one half-life, whereas 25% corresponds to two half-lives. Therefore, Mineral X has undergone more radioactive decay and is older than Mineral Y, assuming the same isotope and closed-system conditions.

Q4. A researcher measures a radioactive parent isotope and finds that 12.5% of the original amount remains. If the isotope's half-life is 2 million years, which reasoning gives the best age estimate?

A.0.25 million years because 12.5% is a small fraction

B.2 million years because any detectable parent isotope indicates one half-life

C.6 million years because three successive half-lives reduce the amount to 12.5% ✅

D.8 million years because 12.5% represents four half-lives

💡 Difficulty: hard | ✅ Correct: C

📖 Explanation: The sequence is 100% to 50% after one half-life, 25% after two, and 12.5% after three. Therefore, three half-lives have passed. Multiplying $3$ by $2$ million years gives an estimated age of $6$ million years.

Q5. A scientist assumes that a newly formed mineral contained no daughter isotope. Later analysis shows that some daughter isotope was already present when the mineral formed. What is the most important consequence?

A.The mineral must be younger than its calculated age

B.Ignoring the initial daughter isotope can produce an inaccurate age estimate ✅

C.The radioactive parent isotope must have stopped decaying

D.The half-life of the parent isotope becomes shorter

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: Radiometric dating calculations often depend on assumptions about the initial amounts of parent and daughter isotopes. If daughter material existed initially but is incorrectly treated as decay-produced, the calculated amount of decay can be overestimated, producing an inaccurate age.

Q6. An archaeological sample is estimated to be 18,000 years old. A dating method uses an isotope with a half-life of 6,000 years. Which observation would provide the strongest support for that estimate, assuming a closed system?

A.Approximately 50% of the original parent isotope remains

B.Approximately 25% of the original parent isotope remains

C.Approximately 12.5% of the original parent isotope remains ✅

D.Approximately 75% of the original parent isotope remains

💡 Difficulty: hard | ✅ Correct: C

📖 Explanation: An age of 18,000 years corresponds to three half-lives because $18,000/6,000=3$ . Starting from 100%, three successive halvings produce 50%, 25%, and finally 12.5% of the original parent isotope.

Q7. A graph of remaining radioactive parent isotope versus time shows a steep decline initially that gradually becomes less steep. Which interpretation is most scientifically appropriate?

A.The isotope's half-life increases continuously with time

B.Radioactive decay follows an exponential pattern, so the absolute amount lost per equal interval decreases ✅

C.The isotope decays linearly until half remains and then stops

D.The mineral becomes younger as the curve becomes flatter

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: Radioactive decay is exponential rather than linear. During equal time intervals, the same fraction of the remaining parent isotope decays, so the absolute quantity lost becomes smaller as less parent material remains. This produces a curve that progressively flattens.

Q8. A student calculates an age by assuming that all daughter isotopes in a rock formed through radioactive decay. Another scientist argues that some daughter isotopes may have entered the rock from its surroundings before measurement. Which error would this create?

A.The calculated age could be artificially increased because excess daughter isotope may be mistaken for decay product ✅

B.The calculated age must be artificially decreased because daughter isotopes accelerate decay

C.The half-life would change because daughter isotopes are present

D.The parent isotope would automatically return to its original amount

💡 Difficulty: hard | ✅ Correct: A

📖 Explanation: If daughter isotope entered the sample from another source, treating all daughter material as radioactive-decay product would make it appear that more parent isotope had already decayed. This can cause the calculated age to be artificially increased.

Q9. A rock sample contains 6.25% of its original radioactive parent isotope. A student claims that only two half-lives have passed because $100\% - 6.25\% = 93.75\%$ decay and therefore the age should be based on 93.75%. What is the error?

A.The student should subtract the remaining percentage from 50%

B.The student incorrectly treats percentage decay as the number of half-lives rather than repeatedly halving the remaining amount ✅

C.The student should multiply 6.25% by the half-life

D.The student assumes radioactive isotopes decay at a constant mass per year

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: The number of half-lives is determined by repeated halving of the remaining parent isotope. The sequence is 100%, 50%, 25%, 12.5%, and 6.25%, so four half-lives have elapsed. Percentage lost cannot be directly equated with the number of half-lives.

Q10. Two dating methods are applied to the same rock. Method A uses an isotope with a half-life of 1,000 years, while Method B uses an isotope with a half-life of 1 billion years. The rock is believed to be about 500 million years old. Which method is more appropriate and why?

A.Method A, because shorter half-lives always produce more precise ages

B.Method B, because its half-life is more suitable for measuring very old material ✅

C.Method A, because nearly all radioactive isotopes remain unchanged for long periods

D.Both methods are equally appropriate regardless of the rock's age

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: For a sample hundreds of millions of years old, an isotope with a billion-year-scale half-life remains measurable and provides useful parent-daughter information. An isotope with a 1,000-year half-life would have undergone essentially complete decay and be unsuitable.

Q11. A researcher obtains these measurements from three samples using the same isotope: Sample P has 50% parent remaining, Sample Q has 25%, and Sample R has 12.5%. Which ranking correctly orders them from youngest to oldest?

A.R, Q, P

B.P, Q, R ✅

C.Q, P, R

D.P, R, Q

💡 Difficulty: easy | ✅ Correct: B

📖 Explanation: Less remaining parent isotope indicates that more radioactive decay has occurred. P has undergone one half-life, Q two, and R three. Therefore, P is the youngest, followed by Q, while R is the oldest of the three.

Q12. A mineral has a measured parent-to-daughter ratio that suggests four half-lives have elapsed. However, geological evidence indicates the mineral experienced a later event that allowed some parent isotope to escape. How should the original radiometric age be interpreted?

A.The calculated age may be unreliable because loss of parent isotope can make the sample appear older ✅

B.The calculated age is definitely accurate because half-life never changes

C.The sample must be younger because parent isotope escaped

D.The daughter isotope will automatically correct the calculation

💡 Difficulty: easy | ✅ Correct: A

📖 Explanation: Radiometric dating assumes that the measured parent and daughter quantities accurately reflect the closed history of the sample. If parent isotope escaped after formation, the remaining parent appears unusually depleted, making the sample seem to have experienced more decay and potentially producing an artificially old age.

Q13. A sample initially contains $160$ units of radioactive parent isotope. After one half-life, a measurement shows $80$ units. After another half-life, the measurement shows $40$ units. A student predicts $0$ units after the third half-life. Why is the prediction incorrect?

A.Radioactive decay produces a fixed amount of parent isotope each half-life

B.Each half-life removes half of the amount remaining, so the third measurement should be

20

units ✅

C.The isotope gains parent atoms during each half-life

D.Half-life applies only to daughter isotopes

💡 Difficulty: easy | ✅ Correct: B

📖 Explanation: A half-life means that half of the radioactive parent atoms present at that time decay, not that the same absolute amount disappears each interval. Thus $160\rightarrow80\rightarrow40\rightarrow20$ , so 20 units should remain after three half-lives.

🔗 Related Topics (MCQs)

📝 Matter, elements and compounds explanation MCQs 📝 Elements vs compounds difference MCQs 📝 Essential elements of life MCQs 📝 Atomic structure determines element properties MCQs 📝 Subatomic particles protons neutrons electrons MCQs

←Previous Topic:Radioactive tracers in biology and medicine📝 Radiometric dating and half lifeElectron energy levels shells:Next Topic→