Nuclear Radius Practice Questions
R  r0 A1/ 3
A1 / 3 
1. Rearrange the equation so that A is the subject.
R
A   
 r0 
R
r0
3
2. Calculate R for Gold (A =197 ) and Carbon (A=12). Use r0 = 1.05 fm. RGold = 6.11 × 10-15m RCarbon
= 2.40 × 10-15m
Calculating Nuclear Density
Radius of a carbon nucleus ~ 3.2 × 10-15m. Radius of a gold nucleus ~ 8.1 × 10-15m. (Calculated using
r0 = 1.40 fm)
Mass of a carbon nucleus ~ 2.00 × 10-26kg. Mass of a gold nucleus ~ 3.27 × 10-25kg.
3. What are the densities of the nuclei?

m

V
m
4 R 3
3
ρGold = 1.47 × 1017 kg m-3 ρCarbon = 1.46 × 1017 kg m-3
4. Calculate the density of a neutron star of radius 25 km and mass = 4 × 1030 kg
ρNS = 4.89 × 1017 kg m-3
5.
(a) If a carbon nucleus containing 12 nucleons has a radius of 3.2 × 10-15m, what is r0?
r0 = 1.40× 10-15 m
r0 
R
A1 / 3
(b) Calculate the radius of a radium nucleus containing 226 nucleons. Use r0 = 1.05 fm.
R = 6.40 × 10-15 m
(c) Calculate the density of a radium nucleus if its mass is 3.75 × 10-25 kg.
ρRadium = 3.42 × 1017 kg m-3
R  r0 A1/ 3

m

V
m
4 R 3
3
6.
A sample of pure gold has a density of 19,300 kg m-3. If the density of the gold nucleus is 1.47 ×
1017 kg m-3 discuss what this implies about the structure of a gold atom.



Most of an atom’s mass is in its nucleus.
The nucleus is small compared to the atom.
An atom must contain a lot of empty space.
Stretch & Challenge
An often quoted random fact is that a sugar cube of a neutron star has mass roughly equal to the
mass of all the humans on Earth.
7. Making some reasonable approximations, show whether or not this is true.
Assumptions
Diameter of a neutron star ~ 25 km.
Mass of a neutron star ~ 4 × 1030 kg
Total number of humans on Earth ~ 6 billion
Average mass of humans ~ 70 kg.
mass of all humans = 6 ×109 × 70 kg = 4.2 × 1011 kg
from Q4 ρNS = 4.89 × 1017 kg m-3, Assume sugar cube volume V = 1 cm3 = 1 × 10-6 m3
m = 4.89 × 1011 kg  so reasonably close!
m  V