The Density of a Nucleus: A Question About Steps in Calculating Nuclear Density

In summary, the conversation discusses a problem with a solution involving the values ρn, mn, Vn, ma, and Ra. The speaker found an error in the solution where the value 10-5 should have been cubed, but it was not. They suggest that the correct value should be (10-5)3 and ρa/(10-5)3. The speaker also mentions double-checking their logic and finding a similar problem with simpler numbers.
  • #1
nmsurobert
288
36
Homework Statement
There is relatively little empty space between atoms in solids and liquids, so that the average density of an atom is about the same as matter on a macroscopic scale—approximately 10^3 kg/m^3 . The nucleus of an atom has a radius about 10^-5 that of the atom and contains nearly all the mass of the entire atom. (a) What is the approximate density of a nucleus?
Relevant Equations
ρ = m/V
I have the solution to the problem but I think I found either a typo or steps that were not included. I think I have made sense of the problem but I would like to double check that I'm doing this right. Thanks.

ρn = mn/Vn

mn ≈ ma

Rn = 10-5Ra

This is were I am having issue. The solution says:

ρn = ma/10-5Va = ρa/10-5

ρn = 103 kg/m3/10-5

It says 10-5Va. Shouldn't it be (10-5)3Va because of the radius is a cubed value? Same for the ρn/10-5. Shouldn't it also be ρa/(10-5)3?

If those values are not cubed then I end up with

ρn = 103 kg/m3/10-5 = 108... which is not right.

But if I cube that value then I get the correct answer. I wrote up a similar problem using simpler numbers and my logic checked out. However, like I said, I just wanted to double check.
 
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  • #2
You are correct. They should have cubed the 10-5.
 
  • #3
TSny said:
You are correct. They should have cubed the 10-5.
awesome. thanks.
 

1. What is the density of a nucleus?

The density of a nucleus varies depending on the type of atom, but on average it is about 2.3 x 10^17 kilograms per cubic meter.

2. How is the density of a nucleus calculated?

The density of a nucleus is calculated by dividing the mass of the nucleus by its volume. The mass of the nucleus can be determined using the atomic mass number, and the volume can be estimated using the radius of the nucleus.

3. Does the density of a nucleus affect its stability?

Yes, the density of a nucleus can affect its stability. Generally, nuclei with higher densities are more stable as they have a stronger nuclear force holding the protons and neutrons together.

4. What factors can affect the density of a nucleus?

The density of a nucleus can be affected by the number of protons and neutrons it contains, as well as the size of the nucleus. The type of atom and its isotopes can also impact the density of the nucleus.

5. How does the density of a nucleus compare to other materials?

The density of a nucleus is incredibly high, making it one of the densest materials in the universe. For comparison, the density of a nucleus is about 10 trillion times greater than the density of water.

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