Dependence of radius on A
R = (1.2×10í^15 m)A1/3
R = nuclear radius
A = mass number
38.7 - Sample problem: nuclear density
Variables
What is the strategy?
- Convert the mass of each nucleus from atomic units to kilograms using the conversion factor stated below.
- Find the radius of each nucleus using the relationship between radius and mass number.
- Calculate the volume of each nucleus using the radius just calculated.
- Divide mass by volume to find the density.
Physics principles and equations
The nuclear radius grows as the cube root of the mass number.
R = (1.2×10í^15 m)A1/3
The nuclear shape may be modeled as a sphere. The volume of a sphere in terms of its radius is
The definition of an atomic mass unit is
u = 1.66 × 10í^27 kgMass density
ȡ = m/V
Calculate the density of the hydrogen
nucleus (A = 1, mass § 1.0 u) and of
an aluminum-27 nucleus (A = 27,
mass§ 27 u). Express the answer in
kg/m^3 , to two significant figures.
mass of hydrogen nucleus mH
radius of hydrogen nucleus RH
volume of hydrogen nucleus VH
mass of aluminum nucleus mAl
radius of aluminum nucleus RAl
volume of aluminum nucleus VAl