The nuclear atom (6.4.1)
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In 1911, Rutherford’s alpha-particle scattering experiment proved that atoms contain a small, positively charged nucleus at the centre.
An alpha particle is a helium-4 nucleus — consisting of two protons and two neutrons.
In Rutherford’s alpha particle scattering experiment, a beam of alpha particles was fired at a thin sheet of gold foil.
The angles at which the alpha particles were scattered by the gold foil were measured by a circular fluorescent screen.
The following observations were made from the alpha particle scattering experiment:
- Most of the alpha particles passed straight through the gold foil (approximately )
- A small fraction of the alpha particles were scattered by an angle greater than (approximately )
- An even smaller fraction of the alpha particles were deflected back toward the source (approximately )
The alpha-particle scattering experiment led Rutherford to the following conclusions about the atom:
- Most of the atom is empty space, since most of the alpha particles passed straight through.
- Most of the mass of the atom is concentrated in the nucleus since the alpha particles had a relatively high momentum and some were still reflected back toward the source.
- The nucleus was positively charged since it repelled the positive alpha particles that passed nearby and caused them to deflect.
The alpha particle scattering experiment determined the existence of the atomic nucleus:
- In 1917, Rutherford determined that the hydrogen nucleus was a single proton.
- Chadwick discovered the neutron in 1933.
- These discoveries led to the nuclear model of the atom, which features a nucleus at the centre surrounded by electrons.
- Niels Bohr later improved this simple model by suggesting that electrons orbit the nucleus at certain distances from the nucleus in electron shells.
The atomic nucleus consists of protons and neutrons:
- Protons are positively charged and neutrons have zero charge so the overall charge of the nucleus is always positive.
- Protons and neutrons have approximately the same mass.
In the nuclear model of the atom, it was determined that:
- Electrons orbit the nucleus in fixed energy levels.
- For every atom the number of electrons is always equal to the number of protons so the overall charge is zero.
- The mass of the electron is equal to approximately that of the proton.
In the alpha particle scattering experiment, Rutherford used the distribution of alpha particles to determine an upper limit on the radius of a gold nucleus as having magnitude
An alpha particle and a gold nucleus are both positively charged, so they repel each other.
When an alpha particle is fired directly at a gold nucleus, it will reach a point of closest approach and then travel back in the opposite direction.
When an alpha particle is fired directly at a positively-charged atomic nucleus, the distance of closest approach can be determined using the principle of conservation of energy.
The alpha particle has maximum kinetic energy when it is fired from a source.
As it travels closer toward the nucleus, the alpha particle experiences a stronger repulsion.
When the alpha particle reaches the point of closest approach, it comes to a stop so its kinetic energy is zero: all of its initial kinetic energy has been converted to electric potential energy
The decrease in kinetic energy is equal to its increase in electric potential energy, so that the sum of the two quantities remains constant and that energy is conserved.
Nuclear radii have now been measured as ranging between to
In the years following the alpha scattering experiment of 1911, X-ray diffraction measurements showed that the atomic radius is approximately five orders of magnitude larger than the nuclear radius.
If the nucleus of an atom were the diameter of a needle head, then the atomic radius would be the length of a football field.
Question walkthrough
Estimating Closest Approach in Alpha Scattering
Estimates the closest approach distance of an alpha particle fired at a gold nucleus by equating its kinetic energy to electric potential energy.
The term nucleon refers to particles inside the nucleus: protons and neutrons:
- The proton and the neutron have approximately the same mass.
- The proton has a charge of where is the elementary charge.
- The neutron has no charge.
An atom has no net charge and has the same number of protons as electrons.
For an element the nucleus of an atom of that element can be represented by nuclear notation.
Where:
- is the nucleon number: the total number of protons and neutrons. is also known as the mass number, since it gives the mass of the nucleus in units of the proton (or neutron) mass.
- is the proton number: the number of protons. is also known as the atomic number, since it determines the type of atom.
Isotopes are atoms of the same element that contain a different number of neutrons in their nuclei.
For example, carbon exists in three naturally occurring isotopes: carbon-12 (six neutrons), carbon-13 (seven neutrons) and carbon-14 (eight neutrons).
- Isotopes of a given element have the same number of protons and hence the same number of electrons, meaning they have the same chemical properties.
- Isotopes of a given element have different masses, meaning they have different physical properties, such as melting point and density.
When using nuclear notation, always label the element with the nucleon and proton numbers.
For example, carbon-14 has six protons and eight neutrons.
Protons are positively charged. Like charges repel, so protons in the atom should repel each other.
The electrostatic force of attraction between two like charges is inversely proportional to the square of the distance between them:
Therefore, as becomes small, such as the spacing between protons in the nucleus, the electrostatic force of repulsion becomes extremely large.
The size of the nucleus is approximately All protons in an atom are squeezed within this small space. This distance of separation corresponds to extremely large electrostatic forces between protons of about
The electrostatic repulsion between protons in the nucleus is balanced by the strong nuclear force. Colloquially referred to as the strong force:
- The strong nuclear force acts between all nucleons (protons and neutrons) equally.
- The strong force is exclusively a short-range force and becomes practically zero when nucleons are separated by distances of about where is a femtometre, or
- The strong force is repulsive at extremely short distances, meaning that the nucleus does not crush itself.
- The strong force is attractive between distances of approximately and
Electrons moving near the speed of light have de Broglie wavelengths of which is small enough to determine the size of nuclear radii, with size of or by electron diffraction.
This correlates to the scales where the strong nuclear force, which binds the nucleons within an atom, is attractive.
The equation for the approximate radius of a nucleus has been determined by electron diffraction experiments.
Where:
- is the nucleon number of the nucleus,
- and is a constant.
Question walkthrough
Approximate Radius of a Proton
Estimates the approximate radius of a single proton using the nuclear radius formula r = r₀A^(1/3) with a mass number of 1.
Nuclei have an extremely large density, of order The density of a nucleus is defined as its mass (in ) divided by its volume (in ).
The density of atomic nuclei is many orders of magnitude greater than the density of everyday materials. For example:
- the density of air is
- the density of water is
- and the density of lead is
Atomic mass units are used to express the mass of atoms and nuclei.
One atomic mass unit is equal to the mass of a neutral carbon-12 atom divided by 12:
- the small difference in mass between the proton and neutron has a significant impact on the binding energy of nuclei.
- it is essential to make accurate calculations of the average atomic mass of an element that exists in a mixture of isotopes.
The mass of a nucleus is approximately given by its nucleon number multiplied by the atomic mass unit, since the proton and neutron each have a mass of approximately
The electron has a mass of approximately
Question walkthrough
Calculating Nuclear Density of Deuterium
Calculates the density of a deuterium nucleus by finding its volume from the nuclear radius formula and dividing by its total nucleon mass.