Why are the lines in the line spectrum of an atom of fixed wavelength and frequency?

Answer 1

First, there is a direct relationship between wavelength and frequency.

Wavelength x frequency = c (the speed of light)

This equation says that for every wavelength or color of light, there is one corresponding frequency at which the electric field of the photon (of that wavelength) oscelates. The two values, wavelength (measured in meters) and frequency (measured in 1/seconds), multiplied together always produce the value of the speed of light (measured in meters/second). Because the speed of light in a vacuum is a constant, any wavelength only has one frequency. When you're measuring the wavelength of light in something other than a vacuum, say air or glass, the wavelength changes slightly, but the frequency does not.

Second, atoms absorb and emit light by letting an electron in one of the outer orbitals jump up to a higher energy orbital, or fall down to a lower energy orbital. Electrons orbit the nucleus of an atom at well defined distances from the nucleus. Their are a number of discrete orbits about which an electron can reside. Electrons can hop from one orbital to another unpopulated orbital by absorbing a photon. Because the orbitals are discrete levels a discrete amount of energy is required to go from a lower orbital to a higher orbital. A photon has a discrete amount of energy that is related to it's frequency as,

Photon Energy = Plank's Constant x Photon Frequency

or

Photon Energy = Plank's Constant x c (speed of light) / Photon Wavelength

When a photon, with energy equal to the gap between the lower electron orbital and the higher electron orbital, is absorbed by the electron, the electron "hops" from the lower to the higher energy orbital.

If a photon with three quarters of the energy needed to bridge the gap between the lower and the higher orbital energy gap interacted with the electron it would not provide enough energy to let the electron "hop" the energy gap. This photon would not be absorbed by the electron because there is no stable electron orbital between the two orbitals. (This is what is meant by discrete. If the orbitals were a 'continuous' band then any photon could be absorbed and the electron could hop to any point in between the lower and higher orbital. Unfortunately orbitals have discrete energy levels.)

If a photon is absorbed by an atom, one of the electrons hops from a lower to a higher orbital. This happens at only one wavelength (or relatively small band of wavelengths in the real world). Atoms want to exist in the ground state if at all possible, so there is a tendency for electrons that are in higher orbitals to want to hop back down to lower orbitals, until all the lowest orbitals are full. (The number orbitals to fill and number of electrons in a ground state atom depend to the number or protons in the nucleus.)

After a photon has been absorbed the electron will remain in the higher orbital, also called an excited state, for a short time before the electron hops back down to the lower or ground state. To account for the energy difference between the higher and lower states a photon of energy equal to the difference in the energy of the two orbitals is emitted by the electron. Again, because the energy levels are discrete, the energy of the photon released will always be the same for that particular transition from a higher to a lower orbital.

Atoms, especially the larger atoms, have many, many orbitals that can hold an electron. There are actually many more discrete orbitals that can hold an electron than there are protons. Each orbital has a discrete energy level and therefore a number of discrete wavelengths or frequencies can be absorbed or emitted in transitions of electrons from one orbital to another. This is why any one atom absorbs and emits photons at a number of discrete wavelengths across a broad spectrum.

Due to factors that exist in the real world, (vibrational energy, thermal energy, and momentum energy, and Doppler shift, to name a few), the absorption spectrum measurements of a particular atom will not show perfectly discrete absorption peaks. There is always some small range of wavelengths about a central peak that are absorbed and emitted. The real world factors have the effect of making the gap between two orbitals a little larger or smaller than the idealized atom at rest in a vacuum. The broadened absorption peaks can have many different shapes depending upon the exact effect being measured. For most spectral characterizations of an element, ignoring the real world factors is often good enough to identify one element and discriminate it from another.

Answer 2

The atom will never split in or with the spectrum it will either reflect off a light or a reflective object and become the colours of the rainbow