The ratio of frac 14 C 12 C in a piece of wood is 1/8 part that of atmosphere. If half life of 14 C is 5730 years, the age of wood sample is \ \ \ \ years.

Chemistry · Chemical Kinetics

JEE Main 2024 — 1 February, Shift 1 — Question 77

The ratio of $\frac{{ }^{14} \mathrm{C}}{{ }^{12} \mathrm{C}}$ in a piece of wood is $\frac{1}{8}$ part that of atmosphere. If half life of ${ }^{14} \mathrm{C}$ is 5730 years, the age of wood sample is $\_\_\_\_$ years.

Answer: 17190

Numerical answer — enter this value.

Step-by-step solution

\text{Given:} \quad \frac{{}^{14}\mathrm{C}}{{}^{12}\mathrm{C}} = \frac{1}{8}, \quad \text{Half-life of } {}^{14}\mathrm{C} = 5730 \text{ years}

\frac{N}{N_0} = \left( \frac{1}{2} \right)^n = \frac{1}{8} \Rightarrow n = 3

\text{Age of wood} = n \times \text{half-life} = 3 \times 5730 = \boxed{17190 \text{ years}}

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Exam: JEE Main 2024
Paper: 1 February, Shift 1
Subject: Chemistry
Chapter: Chemical Kinetics
Topic: Integrated Rate Laws