Chapter 24: Q24.40 P (page 1104)

If $6 .40 \times 10^{- 9} mol$ of $^{176} W$ emits $1 .07 \times 10^{15} β^{+}$ in $1 .00 h$ , what is the decay constant?

Short Answer

Expert verified

The decay constant is $0.325 h^{- 1} .$

Step by step solution

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

The initial amount of $^{176} W$ is as follows:

$\begin{matrix} N_{0} = 6.40 \times 10^{- 9} mol \times \frac{6.022 \times 10^{23} atoms}{1 mol} \\ = 3.854 \times 10^{15} atoms. \end{matrix}$

After $t = 1.00 h, 1.07 \times 10^{15}$ atoms decayed, therefore

$\begin{matrix} N_{t} = N_{0} - 1.07 \times 10^{15} \\ = 3.854 \times 10^{15} atoms - 1.07 \times 10^{15} atoms \\ = 2.784 \times 10^{15} atoms. \end{matrix}$

Now, using this equation, compute the decays constant.

$\begin{matrix} \ln (\frac{N_{t}}{N_{0}}) = - kt \\ k = \frac{- \ln (\frac{N_{t}}{N_{0}})}{t} \\ = \frac{- \ln (\frac{2.784 \times 10^{15} atoms}{3.854 \times 10^{15} atoms})}{1 h} \\ = 0.325 h^{- 1} . \end{matrix}$

Therefore, the computed value is $0.325 h^{- 1} .$

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If $6 .40 \times 10^{- 9} mol$ of $^{176} W$ emits $1 .07 \times 10^{15} β^{+}$ in $1 .00 h$ , what is the decay constant?

Short Answer

Step by step solution

Decay constant

Calculation of the decay constant

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If6.40×10−9mol of 176Wemits1.07×1015β+ in 1.00h, what is the decay constant?

Short Answer

Step by step solution

Decay constant

Calculation of the decay constant

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Chemistry Textbooks

The Earths Atmosphere

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Study anywhere. Anytime. Across all devices.

If $6 .40 \times 10^{- 9} mol$ of $^{176} W$ emits $1 .07 \times 10^{15} β^{+}$ in $1 .00 h$ , what is the decay constant?