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Chapter 24: Q24.37 P (page 1104)

If one-trillionth of the atoms of a radioactive isotope disintegrate each day, what is the decay constant of the process?

Short Answer

Expert verified

The decay constant is $1 \times 10^{- 12} {day}^{- 1} .$

Step by step solution

01

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.

02

Calculation of the decay constant

A: represents the 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.

$A = \frac{1}{1 \times 10^{12}} decays / day. N$

Now, using this equation, compute the decay constant.

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

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

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