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

Short Answer

Expert verified

The mass of \(^{239}{\rm{Pu}}\) that has an activity of\(1.00\,\mu {\rm{Ci}}\) is \(17.2\,\mu {\rm{g}}\).

Step by step solution

01

Definition of mass

Mass is a unit of measurement for the amount of matter in a body.

02

use the radioactive decay law

Consider the given problem and solve.

From appendix A, read the atomic mass number of \({\;^{259}}{\rm{Pu}}\) :

\({A_{{\rm{Pu}}}} = 259\)

From appendix B, read the half life time of \(^{259}{\rm{Pu}}\):

\({t_{1/2}} = 2.41 \cdot {10^4}{\rm{y}}\)

Using the radioactive decay law,

\(R = \frac{{N\ln 2}}{{{t_{1/2}}}}\)

Hence, the fact: \(1\,{\rm{Ci}} = 3.70 \cdot {10^{10}}\,\;{\rm{Bq}}\).

03

Find the mass

Let us solve the given problem.

We obtain,

\(\begin{aligned} N &= \frac{{R{t_{1/2}}}}{{\ln 2}}\\ &= \frac{{1.00 \times {{10}^6} \times 3.70 \times {{10}^{10}}\;{{\rm{s}}^1} \times 2.41 \times {{10}^4} \times 360 \times 24 \times 3600\;{\rm{s}}}}{{0.693}}\\ &= 4.00 \times {10^{16}}\end{aligned}\)

Mass of Plutonium:

\(\begin{aligned} m &= NAu\\ &= 4.00 \times {10^{16}} \times 259 \times 1.66 \times {10^{27}}\;{\rm{kg}}\\ &= 17.2\,\mu {\rm{g}}\end{aligned}\)

Therefore, mass of Plutonium is \(17.2\,\mu {\rm{g}}\).

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Most popular questions from this chapter

The naturally occurring radioactive isotope \(^{{\rm{232}}}{\rm{Th}}\) does not make good fission fuel, because it has an even number of neutrons; however, it can be bred into a suitable fuel (much as \(^{{\rm{238}}}{\rm{U}}\) is bred into\(^{239}P\)).

(a) What are Z and N for\(^{{\rm{232}}}{\rm{Th}}\)?

(b) Write the reaction equation for neutron captured by \(^{{\rm{232}}}{\rm{Th}}\) and identify the nuclide \(^AX\)produced in\(n{ + ^{232}}Th{ \to ^A}X + \gamma \).

(c) The product nucleus \({\beta ^ - }\)decays, as does its daughter. Write the decay equations for each, and identify the final nucleus.

(d) Confirm that the final nucleus has an odd number of neutrons, making it a better fission fuel.

(e) Look up the half-life of the final nucleus to see if it lives long enough to be a useful fuel.

(a) Calculate the energy released in the neutron-induced fission reaction\(n{ + ^{239}}Pu{ \to ^{96}}Sr{ + ^{140}}Ba + 4n\), given \(m{(^{96}}Sr) = 95.921750{\rm{ }}u\)

And

\(m{(^{140}}Ba) = 139.910581{\rm{ }}u\).

(b) Confirm that the total number of nucleons and total charge are conserved in this reaction.

The ruins of the Chernobyl reactor are enclosed in a huge concrete structure built around it after the accident. Some rain penetrates the building in winter, and radioactivity from the building increases. What does this imply is happening inside?

Energy input is required to fuse medium-mass nuclei, such as iron or cobalt, into more massive nuclei. Explain why.

Calculate the energy output in each of the fusion reactions in the proton-proton cycle, and verify the values given in the above summary.

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