Q24.39 P If聽 1.00脳10鈭�12聽molof聽 135C... [FREE SOLUTION]

Chapter 24: Q24.39 P (page 1104)

If $1 .00 脳 10^{鈭� 12} mol$ of $^{135} Cs$ emits $1 .39 脳 10^{5} 尾^{鈭�}$ particles in $1 .00 yr$ , what is the decay constant?

Short Answer

Expert verified

The decay constant is $2.31 脳 10^{7} {yr}^{鈭� 1}$ .

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:

$\begin{matrix} N_{0} = 1.00 脳 10^{鈭� 12} mol 鈰� \frac{6.022 脳 10^{23} atoms}{1 mol} \\ = 6.022 脳 10^{11} atoms. \end{matrix}$

After $t = 1.00 yr, 鈥� 1.39 脳 10^{5} {鈥夆赌夆赌夆赌�}^{135} Cs$ atoms decayed.

Therefore,

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

Now, let us calculate the decay constant

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

Therefore, the computed value is $2.31 脳 10^{7} {yr}^{鈭� 1} .$

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91影视

If $1 .00 脳 10^{鈭� 12} mol$ of $^{135} Cs$ emits $1 .39 脳 10^{5} 尾^{鈭�}$ 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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91影视

If 1.00脳10鈭�12molof 135Csemits1.39脳105尾鈭� 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

Organic Chemistry

Chemical Reactions

Nuclear Chemistry

Ionic and Molecular Compounds

Physical Chemistry

Study anywhere. Anytime. Across all devices.

If $1 .00 脳 10^{鈭� 12} mol$ of $^{135} Cs$ emits $1 .39 脳 10^{5} 尾^{鈭�}$ particles in $1 .00 yr$ , what is the decay constant?