# Assume a constant 14 C/ 12 C ratio of 13.6 counts per minute per gram of living matter. A sample of a petrified tree was found to give 1.2 counts per minute per gram. How old is the tree? (For 14 C, t 1/2 = 5730 years.)

### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243

Chapter
Section

### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243
Chapter 18, Problem 38E
Textbook Problem
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## Assume a constant 14C/12C ratio of 13.6 counts per minute per gram of living matter. A sample of a petrified tree was found to give 1.2 counts per minute per gram. How old is the tree? (For 14C, t1/2 = 5730 years.)

Interpretation Introduction

Interpretation: A constant 14C/12C ratio is given. The counts per min per gram of a petrified tree are given. Age of the tree is to be determined.

Concept introduction: Radiocarbon dating is based on the radioactivity of the nuclide 614C which decays by beta particle production.

In the process of radiocarbon dating, the ratio of radio carbon to the stable carbon in the sample is studied.

To determine: The age of the given tree.

### Explanation of Solution

Explanation

The decay constant can be calculated by the formula given below.

λ=0.693t1/2

Where

• t1/2 is the half-life of nuclide.
• λ is the decay constant.

Substitute the value of t1/2 in the above equation.

λ=0.6935730yrs1λ=1.21×10-4yrs-1_

Explanation

The age of the tree can be calculated by the formula,

t=2.303λlog[NON]

Where,

• λ is the decay constant

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