   Chapter 31, Problem 54PE

Chapter
Section
Textbook Problem

Data from the appendices and the periodic table may be needed for these problems.A tree falls in a forest. How many years must pass before the 14C activity in 1.00 g of the tree’s carbon drops to 1.00 decay per hour?

To determine

In how much time the activity of 1g of C12 drop to 1.00 decay per hour.

Explanation

Given info:

The activity of 1g of C12 drop to 1.00 decay per hour.

Convert decay per hour to decay per second.

1.00 decay per hour=1.003600 decay persecond

The molar atomic mass of C12 is 12g .

The half life of carbon is 1.81×1022sor5730y .

Formula used:

Find the number of atoms present in 1g of C12 ,

N1=mMNA

Equation-1

Here, N1 is the number of atoms in 1g of C12 , m mass of given sample, M molar atomic mass and NA is the Avogadro number.

The initial number of C14 in the given sample is,

Ni=mMNA×abundance

Find the number of atoms involved to produce this present activity.

Nf=R×t120.693

Equation-2

Finally find the time elapsed using formula,

t=In N i N f0.693t12 Equation-3

Calculation:

Find the number of atoms present in 1g of C12 , substitute known values in equation-1

N1=6.023×1023mol-112

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