   Chapter 19, Problem 61AE

Chapter
Section
Textbook Problem

# The mass percent of carbon in a typical human is 18%, and the mass percent of 14C in natural carbon is 1.6 × 10−10%. Assuming a 180-lb person, how many decay events per second occur in this person due exclusively to the β-particle decay of 14C (for 14C, t1/2 = 5730 years)?

Interpretation Introduction

Interpretation: The mass percent of carbon in a typical human body and mass percent of 14C in natural carbon is given. The decay events per second in a 180lb person are to be calculated.

Concept introduction: Nuclei of radioactive element decompose in various ways. There are two major categories. One involves a change in mass number of the decaying nucleus while others do not. Types of radioactive processes include α particle production, β particle production, γ ray production, electron capture and many others.

Explanation

Explanation

To determine: The decay events per second in a 180lb person.

The number of atoms of 14C in 180lb person is 1.18×1015 g atoms_ .

Weight of person is 180lb .

Mass percent of carbon in typical body is 18% .

Therefore, weight of carbon in person’s body =18×180100=32.4 lb

Mass percent of 14C in natural carbon is 1.6×1010% .

Weight of 32.4 lb 14C in natural carbon =1.6×1010×32.4100=5.184×1011 lb

The conversion of lb to g is done as,

1 lb=453.59 g

Therefore, the conversion of 5.184×1011 lb to g is,

5.184×1011 lb=5.184×1011×453.59 g

Molar mass of 14C is 12 g .

Number of atoms of 14C in 12 g=6.023×1023 atoms .

Therefore, number of atoms of 14C in 5.184×1011×453.59 g=6.022×1023×5.184×1011×453.5912=1.18×1015 g atoms_

Explanation

The value of decay constant is 3.835×10-12 seconds-1_ .

The decay constant is calculated by the formula,

λ=0.693t1/2

Where

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

The half life of 14C is 5730 years

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