1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Calculations Involving Binding Energy of Nucleus

  1. Apr 24, 2010 #1
    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:


    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:


    .. 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.
    Last edited: Apr 25, 2010
  2. jcsd
  3. Apr 24, 2010 #2
    Just gone back and looked at this again.

    Using the differential equation calculated, as listed above, I've plugged in the values I know and solved for Z. Have got an answer of [itex]Z=12[/itex].

    So this I assume means I'm looking for whatever is [itex]{}_{12}^{25}?[/itex] which by looking at the periodic table I find that this is [itex]{}_{12}^{25}Mn[/itex] where the 12 just means that's the stable isotope.

    .. am I anywhere near with this?!
    Last edited: Apr 25, 2010
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Calculations Involving Binding Date
Calculating Ion Pairs, Total Charge and Exposure. Yesterday at 3:18 PM
Mixing CP asymmetry calculation Feb 18, 2018
Calculating the time derivative of <p> Feb 18, 2018
Please help with calculation involve solid angle. Jan 9, 2013
Calculating V Involving a Tube Sep 20, 2010