BOHR ATOM AND KIRCHOFF'S LAWS

The Spectrum of Hydrogen

Neils Bohr tried to explain the spectrum of the hydrogen atom. When light beam is aimed at a gas of hydrogen atoms, when the light intercepts the hydrogen atoms, some photons are absorbed by the atoms (going into exciting the atoms) whereas almost all the photons pass right through. And... it is only very specific photon wavelengths that are absorbed from the light beam. On the other hand, already excited hydrogen atoms emit photons. And... they emit the exact same very specific photon wavelengths as are measured in absorption! Why? This was the quandary Bohr solved (at age 23!).

Bohr's Allowed Electron Orbits: Fixed Energies

The electrons that orbit the nucleus in an atom, are strictly confined to allowed orbits. This is like saying that the planets orbiting the Sun cannot just orbit at any distance, but for some reason are allowed only in certain orbits and nowhere else in between. This is a law of quantum mechanics. Basically, the energy of photons and atoms are in reality an integer multiple of a "fundamental unit of energy", called Planck's constant (denoted h). The electron energies must be 1h, 2h, 3h, etc. to very large multiples. What defines the allowed electron orbits in atoms? After much mathematical manipulation, Bohr derived that it is that the angular momentum of the electrons must be an integer multiple of Planck's constant.

Each allowed orbit thus has a precisely defined energy, which is the sum of the electron's orbital velocity and the amount of electric energy binding the electron to the nucleus.

When an electron is in the smallest allowed orbit, its energy state is the lowest (ground state). If an electron is in a larger orbit, its energy state is "excited", at a higher energy.

When a light beam is incident upon an atom, some photons interact with the atom by interacting with the orbiting electron. The interaction results in the electron changing its orbit from one allowed orbit to another allowed orbit.

In any and all interactions, energy is always conserved. That is, the total energy after the interaction is equal to the total energy before the interaction. The form of the energy after can be different than the form of the energy before, but the total amount stays constant.

OK, so when a photon successfully interacts with an electron, the electron moves from one allowed orbit to another and the electron energy changes by an exact amount, which is exactly equal to the energy difference between the two allowed orbits. The photon vanishes- it gave all of its energy to the electron, raising it to a higher energy orbit.

Since energy is conserved, the interacting photon must carry the energy exactly equal to the energy difference of any two allowed orbits or it cannot interact with the atom- it will simply pass right on by. This is because the electron can only move between allowed orbits. If the energy a photon carries is enough to raise an electron half way to the next allowed orbit, well, then there is no interaction, the electron simple stays where it is and the photon passes on by. This is the essence of the Bohr model of the atom.

Each chemical elements (i.e., type of atom, hydrogen, helium, carbon, etc.) has its own set of allowed orbits. The orbital energies and the energy differences between allowed orbits in hydrogen are different and unique than any other atomic species. This is how we can tell what atomic species are present in stars and in gas clouds between the stars. If we see the "spectral fingerprint" of hydrogen, we know that hydrogen is present, even if the object is millions of light years away from us.

Three Laws of Light and Matter

There are three laws of how light and matter interact, they are called Kirchoff's Laws.

• LAW 1: A highly dense gas/plasma or a solid object emits a continuous spectrum.

  The spectrum is called continuous because all colors of the rainbow (all photon wavelengths) are present. However, this spectrum is not equally bright everywhere, but has a distribution of brightness with wavelength. The distribution of light depends only upon the temperature of the dense gas or solid object. To measure the temperature of the object, find the wavelength where the spectrum is the brightest; this behavior is called Wein's Law. The hotter the dense gas or object, the bluer is the light where the brightness of the continuous spectrum peaks. The cooler the dense gas or object, the redder is the light where the brightness of the continuous spectrum peaks. Also, the total energy in the light depends only on the temperature as well.

• LAW 2: A heated low density gas emits an emission spectrum.

  What is meant by heated gas is that the atoms are excited, which is to say that the electrons bound to the atoms are orbiting in higher energy orbits (not the ground state orbits). There are many ways to excite the atoms, for example, if a star is shining on the gas. The wavelengths of the photons emitted by the gas depends upon the type of atoms in the gas. The light is emitted when electrons lose energy and "fall" from higher energy orbits to lower energy orbits. Thus, the emission spectrum only has photons with energies equal to the energy differences of the electron orbits (this is how we know what atoms are in gas clouds in space!).

• LAW 3: A cool low density gas with a continuous spectrum light beam shining through it from directly behind yields an absorption spectrum.

  What is meant by a cool gas is that the atoms are not excited, which is to say that the electrons bound to the atoms are orbiting in their lowest energy orbits (yes, in the ground state orbits). A hot source directly can provide the continuous spectrum, and the atoms in the intervening gas remove (absorb) some of the light. The only light absorbed depends upon the type of atoms in the gas. The light is absorbed when electrons take up the photon energy and change orbits in the atoms, the rest passes through the gas unaltered. Thus, the absorption spectrum is really the continuous spectrum of the hot source behind the gas from which some photon wavelengths are missing photons; these missing photons have energies equal to the energy differences of the electron orbits (again, this is how we know what atoms are in gas clouds in space!).