Table of contents

1. Intro to General Chemistry3h 48m
2. Atoms & Elements4h 16m
3. Chemical Reactions4h 10m
4. BONUS: Lab Techniques and Procedures1h 36m
5. BONUS: Mathematical Operations and Functions48m
6. Chemical Quantities & Aqueous Reactions3h 53m
7. Gases3h 49m
8. Thermochemistry2h 37m
9. Quantum Mechanics2h 58m
10. Periodic Properties of the Elements3h 9m
11. Bonding & Molecular Structure3h 29m
12. Molecular Shapes & Valence Bond Theory1h 57m
13. Liquids, Solids & Intermolecular Forces2h 23m
14. Solutions3h 1m
15. Chemical Kinetics2h 53m
16. Chemical Equilibrium2h 29m
17. Acid and Base Equilibrium5h 1m
18. Aqueous Equilibrium4h 47m
19. Chemical Thermodynamics1h 50m
20. Electrochemistry2h 42m
21. Nuclear Chemistry2h 36m
22. Organic Chemistry5h 7m
23. Chemistry of the Nonmetals2h 39m
24. Transition Metals and Coordination Compounds3h 16m

21. Nuclear Chemistry

Radioactive Half-Life

General Chemistry

21. Nuclear Chemistry

Radioactive Half-Life

Previous problemNext problem

Struggling with General Chemistry?

Join thousands of students who trust us to help them ace their exams!Watch the first video

Multiple Choice

Carbon-14, which is present in all living tissue, radioactively decays via a first-order process. A one-gram sample of wood taken from a living tree gives a rate for carbon-14 decay of 13.6 counts per minute (CPM). If the half-life for carbon-14 is 5720 years, calculate the time it would take for the count rate to decrease to 6.8 CPM.

1430 years

5720 years

11440 years

2860 years

Previous problemNext problem

Verified step by step guidance

Identify that the decay of Carbon-14 is a first-order process, which means the rate of decay is proportional to the amount of Carbon-14 present.

Use the first-order decay formula: \( N(t) = N_0 e^{-kt} \), where \( N(t) \) is the count rate at time \( t \), \( N_0 \) is the initial count rate, \( k \) is the decay constant, and \( t \) is the time.

Calculate the decay constant \( k \) using the half-life formula for first-order reactions: \( k = \frac{\ln(2)}{\text{half-life}} \). Substitute the given half-life of 5720 years into the formula.

Set up the equation using the initial count rate \( N_0 = 13.6 \) CPM and the final count rate \( N(t) = 6.8 \) CPM. Substitute these values into the first-order decay formula to solve for \( t \).

Rearrange the equation to solve for \( t \): \( t = \frac{\ln(N_0/N(t))}{k} \). Substitute the values for \( N_0 \), \( N(t) \), and \( k \) to find the time it takes for the count rate to decrease to 6.8 CPM.