# Homework Help: Calculating Properties of Nucleus

1. Apr 23, 2010

### Lissajoux

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 $m_{n}$

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

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

2. Relevant equations

Within the problem statement and solution attempt.

3. The attempt at a solution

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

2. Average nuclei radius: $r=r_{0}A^{1/3}$ where $r_{0}$ 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. Apr 23, 2010

### zachzach

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.

3. Apr 23, 2010

### Lissajoux

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:

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

3. OK so this is pretty obvious to do then once parts 1. and 2. are sorted out.

4. Apr 23, 2010

### zachzach

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:
$$V=\frac{4}{3}\pi\left({r_{0}A^{1/3}}\right)^{3}$$

5. Apr 23, 2010

### Lissajoux

Is this: $m_{n}=1.67\times10^{-27}kg$ 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 $m_{n}=1.67\times10^{-27}kg$, 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?

6. Apr 23, 2010

### zachzach

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

7. Apr 23, 2010

### Lissajoux

So then:

1. Mass of nucleus expressed by: $$M = A \times M_{n}$$

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

3. Density of nucleus expressed by: $$\rho = \frac{1.67\times10^{-27}}{\frac{4}{3}\pi r_{0}^{3}}\impies$$ simplifies further?!

8. Apr 23, 2010

### zachzach

Yes because you know the value of $$r_{0}$$ right? It is asking for a numerical answer.

9. Apr 23, 2010

### Lissajoux

3. Yes I know the value of $r_{0}$. So can put this in to give me a numerical result for the value of the nucleus density.

2. Can also put value of $r_{0}$ 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.

10. Apr 23, 2010

### zachzach

1. Yep, looks good!

2. Of course, you can put the numerical value of $r_{0}$ into any equation that contains $r_{0}$. Your problem (#2) asks for an expression involving $r_{0}$ and $A$ though.

11. Apr 23, 2010

### Lissajoux

Great! =D

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