# 1.6 Fission  (Page 5/14)

 Page 5 / 14

## Conceptual questions

Explain why the fission of heavy nuclei releases energy. Similarly, why is it that energy input is required to fission light nuclei?

Explain, in terms of conservation of momentum and energy, why collisions of neutrons with protons will thermalize neutrons better than collisions with oxygen.

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?

Since the uranium or plutonium nucleus fissions into several fission fragments whose mass distribution covers a wide range of pieces, would you expect more residual radioactivity from fission than fusion? Explain.

The core of a nuclear reactor generates a large amount of thermal energy from the decay of fission products, even when the power-producing fission chain reaction is turned off. Would this residual heat be greatest after the reactor has run for a long time or short time? What if the reactor has been shut down for months?

How can a nuclear reactor contain many critical masses and not go supercritical? What methods are used to control the fission in the reactor?

Why can heavy nuclei with odd numbers of neutrons be induced to fission with thermal neutrons, whereas those with even numbers of neutrons require more energy input to induce fission?

Why is a conventional fission nuclear reactor not able to explode as a bomb?

## Problem exercises

(a) Calculate the energy released in the neutron-induced fission (similar to the spontaneous fission in [link] )

$n+{}^{\text{238}}\text{U}\to {}^{\text{96}}\text{Sr}+{}^{\text{140}}\text{Xe}+3\mathrm{n,}$

given and $m\left({}^{\text{140}}\text{Xe}\right)=\text{139.92164}$ . (b) This result is about 6 MeV greater than the result for spontaneous fission. Why? (c) Confirm that the total number of nucleons and total charge are conserved in this reaction.

(a) 177.1 MeV

(b) Because the gain of an external neutron yields about 6 MeV, which is the average $BE/A$ for heavy nuclei.

(c) $A=1+\text{238}=\text{96}+\text{140}+1+1+1,\phantom{\rule{0.25em}{0ex}}Z=\text{92}=\text{38}+\text{53},\phantom{\rule{0.25em}{0ex}}\text{efn}=0=0$

(a) Calculate the energy released in the neutron-induced fission reaction

$n+{}^{\text{235}}\text{U}\to {}^{\text{92}}\text{Kr}+{}^{\text{142}}\text{Ba}+2\mathrm{n,}$

given $m\left({}^{\text{92}}\text{Kr}\right)=\text{91}\text{.}\text{926269 u}$ and $m\left({}^{\text{142}}\text{Ba}\right)=\text{141}\text{.}\text{916361}\phantom{\rule{0.25em}{0ex}}\text{u}$ .

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

(a) Calculate the energy released in the neutron-induced fission reaction

$n+{}^{\text{239}}\text{Pu}\to {}^{\text{96}}\text{Sr}+{}^{\text{140}}\text{Ba}+4n,$

given $m\left({}^{\text{96}}\text{Sr}\right)=\text{95}\text{.}\text{921750 u}$ and $m\left({}^{\text{140}}\text{Ba}\right)=\text{139}\text{.}\text{910581 u}$ .

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

(a) 180.6 MeV

(b) $A=1+\text{239}=\text{96}+\text{140}+1+1+1+1,\phantom{\rule{0.25em}{0ex}}Z=\text{94}=\text{38}+\text{56},\phantom{\rule{0.25em}{0ex}}\text{efn}=0=0$

Confirm that each of the reactions listed for plutonium breeding just following [link] conserves the total number of nucleons, the total charge, and electron family number.

Breeding plutonium produces energy even before any plutonium is fissioned. (The primary purpose of the four nuclear reactors at Chernobyl was breeding plutonium for weapons. Electrical power was a by-product used by the civilian population.) Calculate the energy produced in each of the reactions listed for plutonium breeding just following [link] . The pertinent masses are $m\left({}^{\text{239}}\text{U}\right)=\text{239.054289 u}$ , $m\left({}^{\text{239}}\text{Np}\right)=\text{239.052932 u}$ , and $m\left({}^{\text{239}}\text{Pu}\right)=\text{239.052157 u}$ .

${}^{\text{238}}\text{U}+n\phantom{\rule{0.25em}{0ex}}\to {}^{\text{239}}\text{U}+\gamma$ 4.81 MeV

${}^{\text{239}}\text{U}\to {}^{\text{239}}\text{Np}+{\beta }^{-}+{v}_{e}$ 0.753 MeV

${}^{\text{239}}\text{}\text{Np}\to {}^{\text{239}}\text{}\text{Pu}+{\beta }^{-}+{v}_{e}$ 0.211 MeV

The naturally occurring radioactive isotope ${}^{\text{232}}\text{Th}$ 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 ${}^{\text{238}}\text{U}$ is bred into ${}^{\text{239}}\text{P}$ ).

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

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

(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.

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.

(a) What is the thermal nuclear power output in megawatts?

(b) How many ${}^{\text{235}}\text{U}$ nuclei fission each second, assuming the average fission produces 200 MeV?

(c) What mass of ${}^{\text{235}}\text{U}$ is fissioned in one year of full-power operation?

(a) $2\text{.}\text{57}×{\text{10}}^{3}\phantom{\rule{0.25em}{0ex}}\text{MW}$

(b) $8.03×{\text{10}}^{\text{19}}\phantom{\rule{0.25em}{0ex}}\text{fission/s}$

(c) 991 kg

A large power reactor that has been in operation for some months is turned off, but residual activity in the core still produces 150 MW of power. If the average energy per decay of the fission products is 1.00 MeV, what is the core activity in curies?

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