Chapter 24: Q24.38 P (page 1104)

If $2 .8 \times 10^{- 10} %$ of the atoms of a radioactive isotope disintegrate in $1 .0 yr$ , what is the decay constant of the process?

Short Answer

Expert verified

The decay constant value is $2.8 \times 10^{- 12} {year}^{- 1} .$

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.

Calculation of the decay constant

A: Activity, the amount of particles that have degraded during time.

N: Number of particles

k: decay constant

Every day, one trillionth of the atoms dissolve.

$\begin{matrix} A = 2.8 \times 10^{- 10} % decays / year \cdot N \\ = \frac{2.8 \times 10^{- 10} decays / year}{100} \cdot N \\ = 2.8 \times 10^{- 12} decays / year \cdot N. \end{matrix}$

Now, using this equation, compute the decays constant.

$\begin{matrix} A = k \cdot N \\ k = \frac{A}{N} \\ = \frac{2.8 \times 10^{- 12} decays/year \cdot N}{N} \\ = 2.8 \times 10^{- 12} {year}^{- 1} . \end{matrix}$

Therefore, the computed value is $2.8 \times 10^{- 12} {year}^{- 1} .$

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If $2 .8 \times 10^{- 10} %$ of the atoms of a radioactive isotope disintegrate in $1 .0 yr$ , what is the decay constant of the process?

Short Answer

Step by step solution

Definition of decay constant

Calculation of the decay constant

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If2.8×10−10% of the atoms of a radioactive isotope disintegrate in1.0yr , what is the decay constant of the process?

Short Answer

Step by step solution

Definition of decay constant

Calculation of the decay constant

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Chemistry Textbooks

Inorganic Chemistry

Chemical Analysis

Making Measurements

Organic Chemistry

Physical Chemistry

The Earths Atmosphere

Study anywhere. Anytime. Across all devices.

If $2 .8 \times 10^{- 10} %$ of the atoms of a radioactive isotope disintegrate in $1 .0 yr$ , what is the decay constant of the process?