# 8.3.7 Nuclear Density

### Constant Density of Nuclear Material

• Assuming that the nucleus is spherical, its volume is equal to: • Where R is the nuclear radius, which is related to mass number, A, by the equation: • Where R0 is a constant of proportionality
• Combining these equations gives: • Therefore, the nuclear volume, V, is proportional to the mass of the nucleus, A
• Mass (m), volume (V), and density (ρ) are related by the equation: • The mass, m, of a nucleus is equal to:

m = Au

• Where:
• A = the mass number
• u = atomic mass unit
• Using the equations for mass and volume, nuclear density is equal to: • Since the mass number A cancels out, the remaining quantities in the equation are all constant
• Therefore, this shows the density of the nucleus is:
• Constant
• Independent of the radius
• The fact that nuclear density is constant shows that nucleons are evenly separated throughout the nucleus regardless of their size

### Nuclear Density

• Using the equation derived above, the density of the nucleus can be calculated: • Where:
• Atomic mass unit, u = 1.661 × 10–27 kg
• Constant of proportionality, R0 = 1.05 × 10–15 m
• Substituting the values gives a density of: • The accuracy of nuclear density depends on the accuracy of the constant R0, as a guide nuclear density should always be of the order 1017 kg m–3
• Nuclear density is significantly larger than atomic density, this suggests:
• The majority of the atom’s mass is contained in the nucleus
• The nucleus is very small compared to the atom
• Atoms must be predominantly empty space
Close Close

# ## Download all our Revision Notes as PDFs

Try a Free Sample of our revision notes as a printable PDF.

Already a member?