Q24.40 P If聽6.40脳10鈭�9聽mol 聽of聽 176... [FREE SOLUTION]

Chapter 24: Q24.40 P (page 1104)

If $6 .40 脳 10^{鈭� 9} mol$ of $^{176} W$ emits $1 .07 脳 10^{15} 尾^{+}$ in $1 .00 h$ , what is the decay constant?

Short Answer

Expert verified

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

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:

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

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

$\begin{matrix} N_{t} = N_{0} 鈭� 1.07 脳 10^{15} \\ = 3.854 脳 10^{15} atoms 鈭� 1.07 脳 10^{15} atoms \\ = 2.784 脳 10^{15} atoms. \end{matrix}$

Now, using this equation, compute the decays constant.

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

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

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91影视

If $6 .40 脳 10^{鈭� 9} mol$ of $^{176} W$ emits $1 .07 脳 10^{15} 尾^{+}$ 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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91影视

If6.40脳10鈭�9mol of 176Wemits1.07脳1015尾+ 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

Kinetics

The Earths Atmosphere

Organic Chemistry

Chemical Analysis

Ionic and Molecular Compounds

Chemical Reactions

Study anywhere. Anytime. Across all devices.

If $6 .40 脳 10^{鈭� 9} mol$ of $^{176} W$ emits $1 .07 脳 10^{15} 尾^{+}$ in $1 .00 h$ , what is the decay constant?