<< Chapter < Page Chapter >> Page >

Calculating energy from a kilogram of fissionable fuel

Calculate the amount of energy produced by the fission of 1.00 kg of 235 U size 12{ {} rSup { size 8{"235"} } U} {} , given the average fission reaction of 235 U size 12{ {} rSup { size 8{"235"} } U} {} produces 200 MeV.

Strategy

The total energy produced is the number of 235 U size 12{ {} rSup { size 8{"235"} } U} {} atoms times the given energy per 235 U size 12{ {} rSup { size 8{"235"} } U} {} fission. We should therefore find the number of 235 U size 12{ {} rSup { size 8{"235"} } U} {} atoms in 1.00 kg.

Solution

The number of 235 U atoms in 1.00 kg is Avogadro’s number times the number of moles. One mole of 235 U has a mass of 235.04 g; thus, there are ( 1000 g ) / ( 235.04 g/mol ) = 4.25 mol . The number of 235 U size 12{ {} rSup { size 8{"235"} } U} {} atoms is therefore,

4.25 mol 6.02 × 10 23 235 U/mol = 2 . 56 × 10 24 235 U . size 12{ left (4 "." "25"`"mol" right ) left (6 "." "02" times "10" rSup { size 8{"23"} } `"" lSup { size 8{"235"} } "U/mol" right )=2 "." "56" times "10" rSup { size 8{"24"} } `"" lSup { size 8{"235"} } U} {}

So the total energy released is

E = 2 . 56 × 10 24 235 U 200 MeV 235 U 1.60 × 10 13 J MeV = 8.21 × 10 13 J . alignl { stack { size 12{E= left (2 "." "56" times "10" rSup { size 8{"24"} } `"" lSup { size 8{"235"} } U right ) left ( { {"200"`"MeV"} over {"" lSup { size 8{"235"} } U} } right ) left ( { {1 "." "60" times "10" rSup { size 8{ - "13"} } `J} over {"MeV"} } right )} {} #" "=" 8" "." "20" times "10" rSup { size 8{"13"} } `J "." {} } } {}

Discussion

This is another impressively large amount of energy, equivalent to about 14,000 barrels of crude oil or 600,000 gallons of gasoline. But, it is only one-fourth the energy produced by the fusion of a kilogram mixture of deuterium and tritium as seen in [link] . Even though each fission reaction yields about ten times the energy of a fusion reaction, the energy per kilogram of fission fuel is less, because there are far fewer moles per kilogram of the heavy nuclides. Fission fuel is also much more scarce than fusion fuel, and less than 1% of uranium (the 235 U ) size 12{ {} rSup { size 8{"235"} } U} {} is readily usable.

One nuclide already mentioned is 239 Pu size 12{ {} rSup { size 8{"239"} } ital "Pu"} {} , which has a 24,120-y half-life and does not exist in nature. Plutonium-239 is manufactured from 238 U size 12{ {} rSup { size 8{"238"} } U} {} in reactors, and it provides an opportunity to utilize the other 99% of natural uranium as an energy source. The following reaction sequence, called breeding    , produces 239 Pu size 12{ {} rSup { size 8{"239"} } ital "Pu"} {} . Breeding begins with neutron capture by 238 U size 12{ {} rSup { size 8{"238"} } U} {} :

238 U + n 239 U + γ .

Uranium-239 then β decays:

239 U 239 Np + β + v e ( t 1/2 = 23 min) .

Neptunium-239 also β decays:

239 Np 239 Pu + β + v e ( t 1/2 = 2 . 4 d ).

Plutonium-239 builds up in reactor fuel at a rate that depends on the probability of neutron capture by 238 U size 12{ {} rSup { size 8{"238"} } U} {} (all reactor fuel contains more 238 U size 12{ {} rSup { size 8{"238"} } U} {} than 235 U size 12{ {} rSup { size 8{"235"} } U} {} ). Reactors designed specifically to make plutonium are called breeder reactors    . They seem to be inherently more hazardous than conventional reactors, but it remains unknown whether their hazards can be made economically acceptable. The four reactors at Chernobyl, including the one that was destroyed, were built to breed plutonium and produce electricity. These reactors had a design that was significantly different from the pressurized water reactor illustrated above.

Plutonium-239 has advantages over 235 U size 12{ {} rSup { size 8{"235"} } U} {} as a reactor fuel — it produces more neutrons per fission on average, and it is easier for a thermal neutron to cause it to fission. It is also chemically different from uranium, so it is inherently easier to separate from uranium ore. This means 239 Pu size 12{ {} rSup { size 8{"239"} } ital "Pu"} {} has a particularly small critical mass, an advantage for nuclear weapons.

Phet explorations: nuclear fission

Start a chain reaction, or introduce non-radioactive isotopes to prevent one. Control energy production in a nuclear reactor!

Nuclear Fission

Section summary

  • Nuclear fission is a reaction in which a nucleus is split.
  • Fission releases energy when heavy nuclei are split into medium-mass nuclei.
  • Self-sustained fission is possible, because neutron-induced fission also produces neutrons that can induce other fissions, n + A X FF 1 + FF 2 + xn , where FF 1 size 12{"FF" rSub { size 8{1} } } {} and FF 2 size 12{"FF" rSub { size 8{2} } } {} are the two daughter nuclei, or fission fragments, and x is the number of neutrons produced.
  • A minimum mass, called the critical mass, should be present to achieve criticality.
  • More than a critical mass can produce supercriticality.
  • The production of new or different isotopes (especially 239 Pu ) by nuclear transformation is called breeding, and reactors designed for this purpose are called breeder reactors.

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
Practice Key Terms 9

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Physics for the modern world. OpenStax CNX. Sep 16, 2015 Download for free at http://legacy.cnx.org/content/col11865/1.3
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Physics for the modern world' conversation and receive update notifications?

Ask