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Chapter 10: Problem 68

Find the mass of \(^{239} \mathrm{Pu}\) that has an activity of \(1.00 \mu \mathrm{Ci}\).

Short Answer

Expert verified
The mass of Plutonium-239 (\(^{239} \mathrm{Pu}\)) that has an activity of 1.00 microCurie is approximately 0.014 g

Step by step solution

01

Convert the activity in Curie to dps

1 Ci is equivalent to \(3.7 \times 10^{10}\) dps. Therefore, an activity of \(1.00 \mu \mathrm{Ci}\) is equivalent to \(1.00 \mu \mathrm{Ci} \times \frac{3.7 \times 10^{10} \mathrm{dps}}{1 \mathrm{Ci}} \times \frac{1 \mathrm{Ci}}{10^6 \mu \mathrm{Ci}} = 3.7 \times 10^4 \mathrm{dps}\)
02

Convert the activity in dps to number of atoms.

Activity is the rate of decay of a radioactive substance, which is the number of decays per second (dps). If we know the number of decays in one second, we can calculate the total number of atoms in our sample because each atom would decay once. The number of atoms is therefore equal to the activity in dps, which is \(3.7 \times 10^4 \) atoms.
03

Convert the number of atoms to moles using Avogadro's number

A mole of any substance contains \(6.022 \times 10^{23}\) entities (atoms, molecules, etc). Therefore, \(3.7 \times 10^4 \) atoms would be equal to \(\frac{3.7 \times 10^4 \mathrm{atoms}}{6.022 \times 10^{23} \mathrm{atoms/mol}}\) moles.
04

Convert the number of moles to mass using the atomic mass of Pu-239

The atomic mass of Pu-239 is 239.0521634 g/mol. Therefore, the mass of \(3.7 \times 10^4 \mathrm{atoms}\) would be equal to \(\frac{3.7 \times 10^4 \mathrm{atoms}}{6.022 \times 10^{23} \mathrm{atoms/mol}} \times 239.0521634 \mathrm{g/mol}\) g

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Most popular questions from this chapter

Why does the fusion of light nuclei into heavier nuclei release energy?

The electrical power output of a large nuclear reactor facility is 900 MW. It has a 35.0\% efficiency in converting nuclear power to electrical power. (a) What is the thermal nuclear power output in megawatts? (b) How many \(^{235}\) U nuclei fission each second, assuming the average fission produces \(200 \mathrm{MeV}\) ? (c) What mass of \(^{235} \mathrm{U}\) is fissioned in 1 year of full-power operation?

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