A reactor is developing energy at the rate of 32 MW. Calculate the required number of fissions per second of ₉

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{}_{92}U^{235}

Puducherry TnboardTamil Nadu HSC (DGE) Board 2017Subjective· 5mImportance★★★★★

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Concept understanding — Nuclear Fission

Nuclear fission is the process by which a heavy nucleus splits into two smaller nuclei of roughly comparable mass, releasing a very large amount of energy, discovered in 1938 by the German scientists Otto Hahn and Fritz Strassmann (published January 1939; Lise Meitner and Otto Frisch supplied the theoretical fission interpretation the following month), who found that bombarding uranium with a neutron caused it to break apart in this way. The fission process is always accompanied by the release of additional free neutrons, and the released energy is many orders of magnitude greater than any ordinary chemical reaction can produce.

A representative uranium-235 fission reaction is

^{235}_{92}U+{}^{1}_{0}n\ \to\ {}^{236}_{92}U^{*}\ \to\ {}^{141}_{56}Ba+{}^{92}_{36}Kr+3\,{}^{1}_{0}n+Q

Absorbing a slow (thermal) neutron leaves the uranium nucleus in a short-lived excited state, $^{236}_{92}U^{*}$ , which lasts no more than about $10^{-12}$ s before splitting into two "daughter" fragment nuclei plus, on average, about 2.5 free neutrons; working through the mass bookkeeping for a typical fission channel gives an energy release of roughly 200 MeV per event.

Chain reaction. Since each fission produces roughly three fresh neutrons, and each of those neutrons can go on to trigger fission in yet another uranium-235 nucleus, a self-multiplying chain reaction can develop, with the number of fission events growing rapidly (roughly geometrically) generation after generation. Left completely unchecked, this is an uncontrolled chain reaction, releasing its entire stored energy within a tiny fraction of a second - the principle behind the atomic bomb. If instead the average number of neutrons allowed to trigger further fission is deliberately damped down to exactly one per event, the result is a controlled chain reaction that proceeds steadily and can be harnessed for useful power - exactly what happens inside a nuclear reactor. …

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Dividing the reactor's power output by the energy released in a single fission gives the number of fission events needed per second, which works out to $1\times10^{18}$ fissions/s.

Given data

Power developed by the reactor, $P=32\,MW=32\times10^6\,W=3.2\times10^7\,W$ (i.e. $3.2\times10^7$ joules of energy released every second)
Energy released per fission of $_{92}U^{235}$ , $E_f=200\,MeV$

Converting the energy per fission to joules

Using $1\,eV=1.6\times10^{-19}\,J$ :

$E_f=200\,MeV=200\times10^6\,eV\times1.6\times10^{-19}\,J/eV$

$E_f=200\times1.6\times10^{-13}\,J=3.2\times10^{-11}\,J$

Finding the number of fissions per second

Since the reactor's power output is the total energy released per second, and each fission releases $E_f$ joules, the number of fissions occurring each second, $n$ , satisfies

$P=n\times E_f$

$n=\frac{P}{E_f}=\frac{3.2\times10^7}{3.2\times10^{-11}}$

$n=1\times10^{18}\,\text{fissions per second}$

…

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Q.A reactor is developing energy at the rate of 32 MW. Calculate the required number of fissions per second of 92U235{}_{92}U^{235}92​U235. Assume that energy per fission is 200 MeV.

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Q.A reactor is developing energy at the rate of 32 MW. Calculate the required number of fissions per second of ${}_{92}U^{235}$ . Assume that energy per fission is 200 MeV.

Unlock everything free for 14 days