This should be of use to students of Physics and Chemistry.
Energy Levels
In the nuclear model of an atom, the orbiting electrons cannot occupy any possible orbit around the nucleus. Different orbits correspond to different energy levels, and the electrons are restricted to orbits with specific energies.
Though electrons can only occupy allowed energy levels, they can nonetheless change energy by jumping from one energy level to another.
A simple model of the atom is the “planetary model”. The electron orbits the nucleus, containing the protons and neutrons.
Illustrative example : hydrogen atom
The hydrogen atom consists of a proton (which comprises the nucleus with the neutrons) bound to a single electron by the electromagnetic force.
If a hydrogen atom loses the electron, it becomes a positively-charged hydrogen ion.
The table below shows the energy levels for the hydrogen atom.
We can show the energy levels as a diagram below.
A few aspects to note:
(1) The energies have negative values.
Reason:
The potential energy of two objects is zero only when they are at infinite separation. Because there is an attractive force between a proton and an electron, the electron has been moved from infinity until it is in its orbit. Hence the proton–electron system has lost some energy and, since it was zero to start with, it is now negative.
(2) n is known as the principal quantum number.
(3) The ground state is the lowest energy level, which is the energy level corresponding to n = 1 here. It has the most negative energy value and therefore smallest amount of energy. It is the most stable state.
An electron which occupies a certain level on the energy level diagram will have the designated energy of that particular level. For example, if an electon occupies the n=2 level, it should correspond exactly to an energy of −3.39 eV.
It is crucial to appreciate that the energy levels in atoms are quantized – they can only have discrete, finite values. Think of the various energy levels as the steps on a ladder – an electron cannot step on the ‘empty spaces’ in-between 2 energy levels.
Hypothetically, if an energy level diagram is continuous, then the electron can ‘jump’ to any given values within the upper and lower limits of the system.
Excitation occurs when an electron is promoted from a lower energy level to a higher energy level. The energy level 2 can thus be called the first excited state, etc.
Transition between energy levels
When an electron in the atom jumps from the ground state to the first excited state it must gain some energy, and it must be exactly the right amount of energy.
Thus for a hydrogen atom, if an electron wants to jump to n=1 to n=2, then it has to gain 10.19 eV of energy, based on the calculation
(−3.39) − (−13.58) = 10.19 eV
The energy needed to excite an atom can come from absorption of light by the atom. Light is a packet or quantum called a photon.
The energy E carried by a photon is directly proportional to the frequency f of the radiation.
Planck’s equation
E = h f
where h is the Planck constant (6.63 × 10−34 J s), the constant of proportionality when a graph of E against f is plotted.
The corresponding wavelength for the absorption can be calculated by using the wave equation, c = f λ .
When the electron returns from a higher energy level to a lower energy level, it has to lose the exact amount of energy as the energy difference between the two levels. A photon of this energy (with its corresponding wavelength) will be emitted by the atom as a result.
Ionization of the atom occurs if the electron has gained enough energy to jump from the ground state to the infinity state, as result the electron is completely removed from the nucleus. The amount of energy required for this to happen is the (first) ionization energy.
In Physics and Chemistry, the pair of words 'redshift' and 'blueshift' are often used to describe the change in wavelength. Because the wavelength of red is larger than the wavelength of blue, therefore:
Redshift - increase in wavelength
Blueshift - decrease in wavelength
These terms have found common uses in many fields, for example the 'gravitational redshift' in Astrophysics. That, of course, is another story!
by Ed Law
