Thinking about the hydrogen atom, it has a single proton and an electron. Rutherford had described the atom as containing a nucleus where the majority of the mass of the atom is located, and the electrons are outside the nucleus. How the electron existed in the atom was a puzzle to early scientists. Before the electrons behavior was fully understood, physicists believed a negatively charged particle, like the electron, orbiting the positively charged nucleus would have fall into the nucleus, releasing energy as its orbit decayed. But the hydrogen atom was stable. The electron did not decay as classic physics predicted. There was something special about the behavior of the electron in the hydrogen atom (or any electron in any atom).

When a hydrogen atom is excited is gives of light. In the visible region of the electronmagnetic spectrum the light emitted is shown in the figure below.

It consists of lines, it is not continuous like the emission spectrum of white light.

When Balmer, Lyman and Paschen studied the light emitted by an excited hydrogen atom in the visible, ultraviolt and infrared region they each came up with an equation which calculated the frequency of each line in the spectrum. The general equation which calculates any of these lines is given by the Rhydberg equation;


Neils Bohr organized all the information he could gather about the hydrogen atom, and he then made some unique assumptions to develop a model for the hydrogen atom (this is a Shockwave file) which explained the hydrogen atom emission spectrum. His postulates were;

1. The electron in a hydrogen atom moves around the nucleus in a circular orbit with a particular radius.

2. An electron can only exist at certain integral distances from the nucleus. The further the electron is from the nucleus the greater the energy of the electron. Since only orbits of certain radii are allowed the electron can have only certain values of energy.

3. If no light is incident on an atom the electron remains indefinitely in a particular orbit. The electron is said to exist in a particular energy state.

4. When light is incident on the atom the electron can absorb energy and is moved to an orbit further from the nucleus. The electron is said to be excited to a higher energy level. The frequency of the light which excites the electron from one energy level to another is exactly equal to the difference in energy of the two levels.

5. When an electron falls from a high energy level, an orbit far away from the nucleus, to a lower energy level, an orbit close to the nucleus, light is emitted. The energy of the light emitted is equal to the difference in energy between the two energy levels.


You can explore Bohr's model of the hydrogen atom by clicking on this link.

Here is our discussion of the Bohr model using the Shockwave file from lecture on Friday, November 3, 2000.

Click in the picture on the right to start the clip of the lecture.


Bohr was suggesting the energy of the electron was quantized, that is the electron could only exist in certain allowed energy levels.

In order to reproduce the same equations determined empirical by Rydberg and the others, Bohr formulated a model of the hydrogen atom where the electron could only occupy certain energy states called stationary states.

Bohr's mathematical relationship which expressed these ideas is;

Note Rh is = 2.18 x 10-18 J. The negative arises because Bohr assumed that when the electron is removed from the atom the system would be defined as having zero energy. But when the electron is around the nucleus, the system is more stable and therefore, must be at a lower energy. Therefore, the negative sign. 'n' in the equation is a special number called a quantum number. It can only have integer values from 1 to infinity. The quantum number is also a way of labeling each orbit available to the electron. The first orbit is referred to as the ground state, or the state of the atom at its lowest energy.

The equation suggested by Bohr can generate the equation obtained by Rydberg and the others by recalling,

Bohr was also able to calculate the radius of the electron in each of the allowed orbits. These are given by the equation,

r = n2 (5.30 x 10-11 m)

If the energy values of the first 10 orbits are calculated one can see the energy gets closer and closer to zero, and the energy of the orbits as n get larger get closer together. This can best be seen when the energies are plotted on a graph. Simultaneously the radius of the orbit of the electron gets larger and larger. So as the electron gets further away from the nucleus the energy of the electron inthe orbit gets closer to zero.

So if we plot the energy levels for the electron in the hydrogen atom we have a series of levels that look like;


Energy (Joules)



0 J


-0.61 x 10-19



-0.87 x 10-19



-1.36 x 10-19



-2.42 x 10-19



-5.45 x 10-19



-2.18 x 10-18


Note as n increases the difference in energy between subsequent levels gets smaller while the separation between energy levels gets larger. The radius can be though of as the distance of the electron, in the particular energy level, from the nucleus. The electron can occupy any of these energy levels, which are further and further from the nucleus. Bohr's model can now be used to explain the observed emission spectrum for hydrogen. To do this Bohr postulated that the electron could change energy only by going from one energy level to the next. Such a change was called a transition.

The absorption and the emission spectrum of hydrogen could now be explained in the following way. If the electron is in the ground state of the atom and a photon of light of the exact correct frequency (energy) is incident on the atom the electron can absorb the energy of the photon and is excited to a higher energy level, or higher orbit. Later the electron can fall from the orbit of high energy back to the ground state by re-emitting the photon of light of the same frequency as the original photon which excited the electron. For example, if an electron were in the n = 2 energy level and fell to the n = 1 energy level the difference in energy is;

Recall that,

The same value for the first line in the Lyman series of the emission spectrum of the hydrogen atom. The photon that is released in this transition from the n = 2 level to the n = 1 level has a frequency of 2.47 x 1015 sec-1. So the electron falling from any energy level to the n = 1 level reproduces the Lyman series of lines in the emission spectrum of the hydrogen atom. An electron falling from any level to the n = 2 level, reproduces the Balmer series, etc. Remember for the electron to go from a lower energy level to a higher energy level an absorption of energy must occur. But to make the particular transition it must absorb a photon of the exact energy. No more, no less.

When an electron moves from one energy level (stationary state) to another it either absorbs energy or emits energy. When it is in any of the energy levels it does not spontaneously emit energy and spiral into the nucleus.

As accurate as Bohr's model of the atom was in reproducing the discrete lines in the emission spectrum of the hydrogen atom, there was still a problem. As spectroscopic techniques were refined and developed, faint new lines began to appear in the emission spectrum that began to severely tax Bohr's model. In addition, it was shown that Bohr's model we unsuccessful in explaining the emission spectrum of the next element in the periodic table-helium. Bohr's model of the atom was simple, but it is incomplete. What is required is a new and different way to thing of the atom to better understand the messages it is sending us.