How Do You Calculate the Properties of a Nucleus?

[Lissajoux]

Homework Statement

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 $m_{n}=1.67\times10^{-27}kg$

Homework Equations

Within the problem statement and solution attempt.

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.

 

[zachzach]

Homework Statement

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 $m_{n}=1.67\times10^{-27}kg$

Homework Equations

Within the problem statement and solution attempt.

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.

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.

 

[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.

 

[zachzach]

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.

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

 

[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?

 

[zachzach]

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?

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.

 

[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?!

 

[zachzach]

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?!

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

 

[Lissajoux]

3. Yes I know the value of $r_{0}$. So can put this into 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.

 

[zachzach]

3. Yes I know the value of $r_{0}$. So can put this into 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.

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.

 

[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.