How Does Fission Energy Relate to the Semi-Empirical Mass Formula?

[hhhmortal]

Homework Statement

Use the semi-empirical mass formula to show that when an even-even nucleus of large Z undergoes fission into two identical odd-even fragments energy will be liberated provided that the approximate condition:

c1(A) + c2(Z²) + C3(A)^-5/12 > 0

is satisfied and give values for the constants c1, c2 and c3.

Homework Equations

Semi-empirical mass formula

The Attempt at a Solution

Do I use an example of any atom which is even-even and two other atoms which are odd-even. Then put it into the semi-empirical mass formula and then what exactly do I need?

 

[hhhmortal]

^Bump

 

[Avodyne]

No, you need to demonstrate that it's true for any even-even nucleus of large Z and A decaying into two identical odd-even fragments (so what would the Z and A values of each fragment be?).

 

[hhhmortal]

No, you need to demonstrate that it's true for any even-even nucleus of large Z and A decaying into two identical odd-even fragments (so what would the Z and A values of each fragment be?).

The N = odd and Z= even for both identical fragments. But how would this help me?

 

[soxymoron]

I'm having problems with the same question.

My thinking so far:

Each of the new nuclei will have 1/2A and 1/2Z

For energy to be released the binding energy of the intial nuclei must be greater than two times the binding energy for one of the resultant nuclei.

The odd-even means that the last term of the semi-empirical mass formula is 0, for even-even if delta(Z,A) is 1

I've tried setting this up as an inequality and rearranging but I can't see how an A^(-5/12) would be arrived at. Are there terms that can be neglected for a large Z or was that just in the question to show the SEMF would be accurate in this case?