Chapter 24: Q24.39 P (page 1104)

If $1 .00 \times 10^{- 12} mol$ of $^{135} Cs$ emits $1 .39 \times 10^{5} β^{-}$ particles in $1 .00 yr$ , what is the decay constant?

Short Answer

Expert verified

The decay constant is $2.31 \times 10^{7} {yr}^{- 1}$ .

Step by step solution

Definition of decay constant

The size of a population of radioactive atoms and the pace at which the population diminishes due to radioactive decay are proportionate.

Calculate the decay constant

The initial amount of $^{135} C$ is:

$\begin{matrix} N_{0} = 1.00 \times 10^{- 12} mol \cdot \frac{6.022 \times 10^{23} atoms}{1 mol} \\ = 6.022 \times 10^{11} atoms. \end{matrix}$

After $t = 1.00 yr, 1.39 \times 10^{5}^{135} Cs$ atoms decayed.

Therefore,

$\begin{matrix} N_{t} = N_{0} - 1.39 \times 10^{5} \\ = 6.023 \times 10^{11} atoms - 1.39 \times 10^{5} atoms \\ = 6.02199861 \times 10^{11} atoms. \end{matrix}$

Now, let us calculate the decay constant

role="math" localid="1663381581251" $\begin{matrix} \ln (\frac{N_{t}}{N_{0}}) = - kt \\ k = \frac{- \ln (\frac{N_{t}}{N_{0}})}{t} \\ = \frac{- \ln (\frac{6.02199861 \times 10^{11} atoms}{6.022 \times 10^{11} atoms})}{1 yr} \\ = 2.31 \times 10^{7} {yr}^{- 1} . \end{matrix}$

Therefore, the computed value is $2.31 \times 10^{7} {yr}^{- 1} .$

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If $1 .00 \times 10^{- 12} mol$ of $^{135} Cs$ emits $1 .39 \times 10^{5} β^{-}$ particles in $1 .00 yr$ , what is the decay constant?

Short Answer

Step by step solution

Definition of decay constant

Calculate the decay constant

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If 1.00×10−12molof 135Csemits1.39×105β− particles in1.00yr , what is the decay constant?

Short Answer

Step by step solution

Definition of decay constant

Calculate the decay constant

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Chemistry Textbooks

The Earths Atmosphere

Ionic and Molecular Compounds

Kinetics

Organic Chemistry

Making Measurements

Chemical Analysis

Study anywhere. Anytime. Across all devices.

If $1 .00 \times 10^{- 12} mol$ of $^{135} Cs$ emits $1 .39 \times 10^{5} β^{-}$ particles in $1 .00 yr$ , what is the decay constant?