Calculating Nuclear Binding Energy: Fission of Uranium (A = 238)

[eprparadox]

Homework Statement

The Uranium (A = 238) nucleus has a binding energy of about 7.6 MeV per nucleon. If the nucleus were to fission into two equal fragments, each would have a kinetic energy of just over 100 MeV. From this, it can be concluded that

A) Uranium (A = 238) cannot fission spontaneously
B) Uranium (A = 238) has a large neutron excess
C) nuclei near A = 120 have masses greater than half that of Uranium (A = 238)
D) nuclei near A = 120 must be bound by about 6.7 MeV/nucleon
E) nuclei near A = 120 must be bound by about 8.5 MeV/nucleon

Homework Equations

conservation of mass-energy:
Binding Energy + rest mass of uranium = rest masses of two equal fragments + 100 MeV for each fragment + Binding energy of each fragment

The Attempt at a Solution

So I know that the equation I should write is (using approximate values for the mass numbers):

240*-7.6 + Mc^2 = 2mc^2 + 200 MeV + 240*X

X -> the binding energy of the fragments.
Mc^2 -> rest mass of Uranium
2mc^2 -> rest masses of the two equal fragments created

There is a solution to this problem online, however they neglected to include the rest mass terms on both sides of the equation. I'm a little confused as to why. Is that just because this is an approximate calculation and the rest masses will more or less cancel out on each side?

Any clarification there would be great. Thanks.

 

[anathema]

Thank you for your question. I am a scientist and I would be happy to help you with your confusion.

Firstly, you are correct in setting up the equation as (using approximate values for the mass numbers):

240*-7.6 + Mc^2 = 2mc^2 + 200 MeV + 240*X

However, the reason the rest mass terms are neglected on both sides of the equation is because they are equal and opposite, and therefore they cancel out. This is because the rest mass of the uranium nucleus is equal to the sum of the rest masses of the two equal fragments created.

In other words, the rest mass terms on both sides of the equation represent the same quantity, so they can be omitted. This does not affect the overall solution to the problem.

I hope this helps to clarify your confusion. Please let me know if you have any further questions.
Scientist