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Homework Help: Calculating Properties of Nucleus

  1. Apr 23, 2010 #1
    1. The problem statement, all variables and given/known data

    1. Write down an approximate expression for the mass of a nucleus in terms of mass number A and nucleon mass [itex]m_{n}[/itex]

    2. Assuming that the nucleus is spherical, find an expression for the volume of this nucleus in terms of A and [itex]r_{0}[/itex]

    3. Find a numerical value for the density of the nucleus. Use [itex]m_{n}=1.67\times10^{-27}kg[/itex]

    2. Relevant equations

    Within the problem statement and solution attempt.

    3. The attempt at a solution

    1. I have that nuclear mass is [itex]M=A[/itex], but I don't see where [itex]m_{n}[/itex] factors in.

    2. Average nuclei radius: [itex]r=r_{0}A^{1/3}[/itex] where [itex]r_{0}[/itex] is a defined constant.

    3. Obviously density is mass over volume. Using the value in part 2 for the radius, can calculate the volume of the spherical nucleus. Using this and the value of the nucleus mass given, can calculate the volume. But I don't know what A is in order to be able to get a numerical value.
     
  2. jcsd
  3. Apr 23, 2010 #2
    1. What is the mass number?? Hint: It does not have units of mass.

    2. You didn't find the volume.

    3. Just divide answer from 1 with 2 to get the density.
     
  4. Apr 23, 2010 #3
    1. A = Mass Number = Number of Nucleons = Number of Protons + Number of Neutrons

    I don't see what's going on here, how I can get the expression or any values to get an actual numerical answer.

    2. So I have the radius, and can work out the volume as:

    [tex]V=\frac{4}{3}\pi\left({r_{0}A^{1/3}}\right)^{2}[/tex]

    3. OK so this is pretty obvious to do then once parts 1. and 2. are sorted out.
     
  5. Apr 23, 2010 #4
    1. If I have 5 bowling bowls and each bowling ball weighs 10 pounds and i put them all in one box. How much would the box weigh? You know how much each nucleon weighs.

    2. I think you meant:
    [tex]V=\frac{4}{3}\pi\left({r_{0}A^{1/3}}\right)^{3}[/tex]
     
  6. Apr 23, 2010 #5
    Is this: [itex]m_{n}=1.67\times10^{-27}kg[/itex] the mass of the nucleus or the mass of an individual nucleon? I think it's the latter, but I've got a bit confused now.

    1. So using [itex]m_{n}=1.67\times10^{-27}kg[/itex], multiply this by A to get the mass of the nucleus? I don't know the value of A though.

    2. Yes that is what I meant, it was a typo in the formula. So I can use the mass that I've just calculated in part 1, and the radius from initial question part 2, yep?
     
  7. Apr 23, 2010 #6
    1.Write down an approximate expression for the mass of a nucleus in terms of mass number A and nucleon mass [itex]m_{n}[/itex]. It is not asking for a value in this question just an expression. You have A nucleons and you know the mass of each.

    3. Yep and it looks like the A's will cancel.
     
  8. Apr 23, 2010 #7
    So then:

    1. Mass of nucleus expressed by: [tex]M = A \times M_{n}[/tex]

    2. Volume of nucleus expressed by: [tex]V = \frac{4}{3}\pi\left({r_{0}A^{1/3}}\right)^{3} = \frac{4}{3}\pi r_{0}^{3}A[/tex]

    3. Density of nucleus expressed by: [tex]\rho = \frac{1.67\times10^{-27}}{\frac{4}{3}\pi r_{0}^{3}}\impies [/tex] simplifies further?!
     
  9. Apr 23, 2010 #8
    Yes because you know the value of [tex] r_{0}[/tex] right? It is asking for a numerical answer.
     
  10. Apr 23, 2010 #9
    3. Yes I know the value of [itex]r_{0}[/itex]. So can put this in to give me a numerical result for the value of the nucleus density.

    2. Can also put value of [itex]r_{0}[/itex] into the equation for the nucleus volume, I think that will just make things look worse though than the nice expression there in terms of it.
     
  11. Apr 23, 2010 #10
    1. Yep, looks good!

    2. Of course, you can put the numerical value of [itex]r_{0}[/itex] into any equation that contains [itex]r_{0}[/itex]. Your problem (#2) asks for an expression involving [itex]r_{0}[/itex] and [itex]A[/itex] though.
     
  12. Apr 23, 2010 #11
    Great! =D

    In regards to 2. I think will leave it in terms of [itex]r_{0}[/itex] and maybe just state the value of it seperately below.
     
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