Physics

Problem

^{239}_{94}\mathrm{Pu}

nucleus absorbs a neutron to form an excited

^{240}_{94}\mathrm{Pu}^{*}

state which immediately undergoes fission as shown below:

^{239}_{94}\mathrm{Pu}+^{1}_{0}\mathrm{n}\;\longrightarrow\;^{240}_{94}\mathrm{Pu}^{*}\;\longrightarrow\;^{95}_{36}\mathrm{Kr}+^{144}_{58}\mathrm{Ce}+y\,^{1}_{0}\mathrm{n}+Q

Atomic masses (in u):

^{239}_{94}\mathrm{Pu}:\;239.052163

^{1}_{0}\mathrm{n}:\;1.008665

^{95}_{36}\mathrm{Kr}:\;94.919359

^{144}_{58}\mathrm{Ce}:\;143.913644

1\,\text{u}=931.5\,\text{MeV}/c^{2}

(a) Determine the value of

y

that balances nucleon number and charge. (b) Calculate the energy

Q

released per fission event in

\text{MeV}

. (c) If

1.0\,\text{kg}

^{239}\mathrm{Pu}

were completely fissioned through this process, estimate the total energy released in

\text{kWh}

. (Avogadro number

N_{A}=6.02\times10^{23}\,\text{mol}^{-1}

.) a. (a) Find the value of

y

so that the fission reaction is balanced for both mass number and charge. b. (b) Using the atomic masses given, calculate the

Q

-value (in MeV) of the fission reaction. c. (c) Estimate the total energy that would be released, in kWh, if

1.0\,\text{kg}

^{239}\mathrm{Pu}

were completely fissioned as per this reaction.