(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The binding energy of a nucleus is given by:

[tex]E_{b}=a_{1}A-a_{2}A^{\frac{2}{3}}-a_{3}Z^{2}A^{-\frac{1}{3}}-a_{4}\left(Z-\frac{A}{2}\right)^{2}A^{-1}\pm a_{5}A^{-\frac{1}{2}}[/tex]

For a given set of isobars, [itex]A[/itex] constant, [itex]E_{b}[/itex] will be maximised at the value of [itex]Z[/itex] that satisfies:

[tex]\frac{dE_{b}}{dZ}=0[/tex]

a) Find this derivative and solve for [itex]Z[/itex] in terms of the [itex]a_{i}[/itex] and [itex]A[/itex]

b) Using the expression derived in part a) and given values of [itex]a_{i}[/itex], find the value of [itex]Z[/itex] which maximises [itex]E_{b}[/itex] when [itex]A=25[/itex]. Round [itex]Z[/itex] to the nearest integer value.

c) Use the periodic table and the derived value of [itex]Z[/itex] from part b) to determine which element of mass number 25 is a stable isotope.

2. Relevant equations

Within the problem statement and subsequent solution attempt.

3. The attempt at a solution

a) This is what I have for the differentiated equation:

[tex]\frac{dE_{b}}{dZ}=-2Za_{3}A^{-\frac{1}{3}}-a_{4}\left(2ZA^{-1}-1\right)=0[/tex]

.. this is correct? I think that's all I have to do for this part.

b) I know what the values of [itex]A, a_{3}, a_{4}[/itex] are, so I can put these into the equation, but then how to I 'solve it for Z' from that? I guess that need to find a value of [itex]Z[/itex] such that [itex]\frac{dE_{b}}{dZ}=0[/itex] right? Not sure how to do this.

c) Once I know what [itex]Z[/itex] is, how do I determine which element of mass number 25 is a stable isotope? I don't really understand this question part.

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# Homework Help: Calculations Involving Binding Energy of Nucleus

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