Question

After absorbing a neutron, a Uranium-235 nucleus can fission to produce Barium-141 and krypton-92. Calculate the energy that would be released from this fission of a Uranium-235 atom. How do you work this out?

Answer 1

`1.81*10^17 J`

Explanation:

To solve this question we require some extra information which is not provided but I will take variables in place of them .

`1^(st)` method :

Mass defect method
we must be given the mass of protons and that of neutrons which is not provided so we will take the values provided over internet .

`1 "Proton"=1.00727"amu"`
`1 "Neutron"=1.00866 "amu"`

Net mass of `U^235=92*1.00727+143*1.00866=236.90722 U`

similarly we calculate the mass of barium and krypton ,
`Ba^141=56*1.00727+85*1.00866=142.14322 U`
`Kr^92=36*1.00727+56*1.00866=92.74668 U`

Mass defect(`DeltaM`) =`236.90722 -142.14322-92.74668=2.01732 U`
now according to Einsteins mass energy relation we know

`E=Mc^2`

it can be written as `E=DeltaMc^2=(M(U^235)-M(Ba^141)-M(Kr^92))c^2=2.01732*(3*10^8)=1.81*10^17 J`
this is the case when both the daughter nuclei are not radioactive but if they are we subtract the mass of two neutrons and then multiply by `c^2`.

Answer 2

For the reaction stated, the mass defect is:

`Delta m = (m_U + m_n) - (m_(Ba) + m_(Kr))`

Using rounded amu figures found on Wikipedia:

`= ( (235.044 + 1.008) - (140.914 + 91.926) )`

`approx 3.212 \ "amu"`

A mass of 1 amu converts to energy via `E = mc^2` as: `1 "amu" approx 931 MeV`

So here:

`E approx 3 GeV`

That's about `4.8 xx 10^(-7) J`