Size of the Nucleus
1. Estimating the Size of the Nucleus
- Rutherford's gold foil experiment (1911) showed that the nucleus is extremely small compared to
the atom.
- Electron scattering experiments confirm nuclear sizes in the femtometer (fm) range.
2. Nuclear Radius Formula
The nuclear radius (R) is given by:
R = R0 A^(1/3)
where:
- R0 is the nuclear radius constant (~1.2 to 1.4 femtometers, 10^-15 m).
- A is the mass number (total protons + neutrons).
Examples:
- Hydrogen nucleus (A = 1): R ~ 1.2 fm
- Oxygen nucleus (A = 16): R ~ 3.0 fm
- Uranium nucleus (A = 238): R ~ 7.4 fm
3. Nuclear Density
- Nuclear density remains nearly constant for all elements.
- Density formula:
Density = Mass of Nucleus / Volume of Nucleus
Approximating the nucleus as a sphere:
V = (4/3) pi R^3
The approximate nuclear density is:
rho ~ 2.3 x 10^17 kg/m^3
This is extremely dense, comparable to neutron stars.
1. Estimating the Size of the Nucleus
- Rutherford's gold foil experiment (1911) showed that the nucleus is extremely small compared to
the atom.
- Electron scattering experiments confirm nuclear sizes in the femtometer (fm) range.
2. Nuclear Radius Formula
The nuclear radius (R) is given by:
R = R0 A^(1/3)
where:
- R0 is the nuclear radius constant (~1.2 to 1.4 femtometers, 10^-15 m).
- A is the mass number (total protons + neutrons).
Examples:
- Hydrogen nucleus (A = 1): R ~ 1.2 fm
- Oxygen nucleus (A = 16): R ~ 3.0 fm
- Uranium nucleus (A = 238): R ~ 7.4 fm
3. Nuclear Density
- Nuclear density remains nearly constant for all elements.
- Density formula:
Density = Mass of Nucleus / Volume of Nucleus
Approximating the nucleus as a sphere:
V = (4/3) pi R^3
The approximate nuclear density is:
rho ~ 2.3 x 10^17 kg/m^3
This is extremely dense, comparable to neutron stars.
