Energy released in fission

Thread Starter

circuit2000

Joined Jul 6, 2006
33
Consider the following problem:
1) Calculate the energy released in the fission reaction,
Uranium(235,92) + neutron--->[Uranium(235,92)]*--->Neodymium(143,60) + Zirconium(90,40)+ 3 neutrons + 8 electrons +8 antineutrino
Solution:
If atomic rest masses are used in calculating the Q value, the term 8 e- may be dropped.Let M(U),M(Nd),M(Zr) and M(n) be the atomic masses of Uranium, Neodymium,Zirconium and neutron respectively.
Hence,
Q=[M(U) - M(Nd) - M(Zr) - {3-1}M(n)]c^2
Q= 197.6 MeV
This is the solution given in Schaums book on Modern Physics.
Just because atomic rest masses are used, how can we neglect the 8 e- term?
 

Papabravo

Joined Feb 24, 2006
14,253
Because it is so small when compared to the masses of everything else. The rest mass of an electron is about 0.0005 the mass of a proton. So you do the math.
 

recca02

Joined Apr 2, 2007
1,214
well can u give me the masses used for the calculations?
i believe neglecting 8 e wud mean abt 4.05 Mev of non negligible energy error,
u will have to think of it like;
in a beta(-) decay a neutron is converted into proton;
hence the energy in that case is calculated by
Q=(m(a,z) - M(a,z+1))*931.5Mev;
here the mass of M(a,z+1) has i electron extra in its orbit hence taking atomic mass of m(a,z+1) accounts for the electron mass automatically no need for adding it separately.
similarly,
look carefully in the example problem;
8 neutrons have been converted into 8 protons;
hence electron masses are already accounted for by just subtracting atomic masses,
getting my point? (the atomic masses are such that u dont have to worry abt 8 e )

example:
say a beta emission takes Br(87,35)---Beta(-)--->Kr(87,36) +e-
now if mass of Kr is taken as atomic mass mass of 36 electrons are added (the confusion arises as the above Kr is not a atom but a nucleus so electron evolved is shown separately )
understand it this way (it might be wrong but good for understanding)
atomic mass of Kr = nucleus mass + electrons mass = mass of neutrons + mass of protons + mass of electrons
=(A-Z)(n) +Z(hydrogen)
 
Top