<< 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.

Got questions? Get instant answers now!

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

how do you get the 2/50
Abba Reply
number of sport play by 50 student construct discrete data
Aminu Reply
width of the frangebany leaves on how to write a introduction
Theresa Reply
Solve the mean of variance
Veronica Reply
Step 1: Find the mean. To find the mean, add up all the scores, then divide them by the number of scores. ... Step 2: Find each score's deviation from the mean. ... Step 3: Square each deviation from the mean. ... Step 4: Find the sum of squares. ... Step 5: Divide the sum of squares by n – 1 or N.
kenneth
what is error
Yakuba Reply
Is mistake done to something
Vutshila
Hy
anas
hy
What is the life teble
anas
hy
Jibrin
statistics is the analyzing of data
Tajudeen Reply
what is statics?
Zelalem Reply
how do you calculate mean
Gloria Reply
diveving the sum if all values
Shaynaynay
let A1,A2 and A3 events be independent,show that (A1)^c, (A2)^c and (A3)^c are independent?
Fisaye Reply
what is statistics
Akhisani Reply
data collected all over the world
Shaynaynay
construct a less than and more than table
Imad Reply
The sample of 16 students is taken. The average age in the sample was 22 years with astandard deviation of 6 years. Construct a 95% confidence interval for the age of the population.
Aschalew Reply
Bhartdarshan' is an internet-based travel agency wherein customer can see videos of the cities they plant to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400 a. what is the probability of getting more than 12,000 hits? b. what is the probability of getting fewer than 9,000 hits?
Akshay Reply
Bhartdarshan'is an internet-based travel agency wherein customer can see videos of the cities they plan to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400. a. What is the probability of getting more than 12,000 hits
Akshay
1
Bright
Sorry i want to learn more about this question
Bright
Someone help
Bright
a= 0.20233 b=0.3384
Sufiyan
a
Shaynaynay
How do I interpret level of significance?
Mohd Reply
It depends on your business problem or in Machine Learning you could use ROC- AUC cruve to decide the threshold value
Shivam
how skewness and kurtosis are used in statistics
Owen Reply
yes what is it
Taneeya
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
Practice Key Terms 9

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College physics' conversation and receive update notifications?

Ask