Q24.41 P The isotope聽 21283Bi聽has a hal... [FREE SOLUTION]

Chapter 24: Q24.41 P (page 1104)

The isotope ${^{212}}_{83} Bi$ has a half-life of $1.01$ yr. What mass (in mg) of a $2.00$ -mg sample will remain after ${3.75脳10}^{3} h$ ?

Short Answer

Expert verified

The amount of ${^{212}}_{83} Bi$ that remains is $1.49 mg$

Step by step solution

Radioactive decay

The radioactive decay follows the first order kinetics. The relation between the rate constant and the half-life of the reaction is as shown below:

$k = \frac{0.693}{t_{1 / 2}}$

Calculation

- The half-life of $_{83}^{212} {Biist}_{1/2} =1.01yr$

- The initial amount of $_{83}^{212} {BiwasN}_{0} =2.00mg$

We have to find the mass of $_{83}^{212} Bi$ after time_{$t = 3.75 鈰� 10^{3} h$}

First, let us convert the time elapsed from hours to years

_{$t = 3.75 脳 10^{3} h 脳 \frac{1 d}{24 h} 脳 \frac{1 yr}{365 d} = 0.428 yr$}

Now, let us calculate the decay constant of_{$_{83}^{212} Bi$}

_{$k= \frac{ln(2)}{t_{1/2}} = \frac{0.693}{1.01yr} {=0.686yr}^{-1}$}

Therefore, the amount of ${^{212}}_{83} Bi$ that remains after time t is

_{$\begin{matrix} ln (\frac{N_{t}}{N_{0}}) =-kt \\ ln (\frac{N_{t}}{2.00mg}) {=-0.686yr}^{-1} 脳0.428测谤 \\ =-0.2936 \end{matrix}$}

_{\ $\begin{matrix} \frac{N_{t}}{2.00mg} {=e}^{-0.2936} \\ \frac{N_{t}}{2.00mg} =0.7456 \\ N_{t} =1.49mg \end{matrix}$}

Hence,the amount of ${^{212}}_{83} Bi$ that remains is $1.49 鈥尘驳$ _.

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The isotope ${^{212}}_{83} Bi$ has a half-life of $1.01$ yr. What mass (in mg) of a $2.00$ -mg sample will remain after ${3.75脳10}^{3} h$ ?

Short Answer

Step by step solution

Radioactive decay

Calculation

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91影视

The isotope 21283Bihas a half-life of1.01 yr. What mass (in mg) of a2.00 -mg sample will remain after3.75脳103h ?

Short Answer

Step by step solution

Radioactive decay

Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Chemistry Textbooks

Kinetics

Chemistry Branches

The Earths Atmosphere

Chemical Reactions

Ionic and Molecular Compounds

Inorganic Chemistry

Study anywhere. Anytime. Across all devices.

The isotope ${^{212}}_{83} Bi$ has a half-life of $1.01$ yr. What mass (in mg) of a $2.00$ -mg sample will remain after ${3.75脳10}^{3} h$ ?