In Chapter 2 we explored some of the experimental evidence which has lead to our modern view of the electronic structure of the atom. The atom contains protons, neutrons and electrons

Rutherford is credited with our current view of the atom..a nucleus containing the majority of the mass of an atom made up of protons and neutrons with the electrons outside the nucleus. Our goal in this chapter is gain a better understanding of the model of the electron's behavior.

Classically the electron was viewed as `orbiting' the nucleus. The concept of an orbit, like the moon travelling around the earth, suggests a defined path which allows the exact determination of the position of the moon. It allows up to predict exactly were the moon will rise and at what time each day. Our modern view of the electron differs from this model. Actually the electron occupies an `orbital' and instead of being able to predict where the electron is relative to the nucleus, our model of the electron requires us to think of the probability of finding the electron at a certain position around the nucleus. The electron occupies an orbital and the orbital has 3-dimension shape. The electron has a high probability of being found within the 3-dimensional space defined by the orbital. There are several different types of orbitals which an electron can occupy, and each different type has a different 3-dimensional structure.

Why do we use a 3-dimensional probability distribution (orbital) to describe the electron rather than a 2-dimensional orbit? The reason lies in our view of the nature of the electron. In our previous discussion of the electron and its discovery by J.J. Thomson we describe the electron in terms of its particle properties. we thought of it in terms of its charge and its mass. However, subsequent experiments by Thomson and others revealed a dual nature of the electron. It could also exhibit wave properties. Wave properties which suggested it behaved like light.

So how do we view light and its wave properties? First we'll discuss wave properties (Shockwave file) then we'll look at light. Light that our eyes are able to dedect is only a small part of the total range of electromagnetic radiation. The electromagnetic spectrum (Shockwave file) (Physics WEB Site) shows the range and where visible light is located. Wave motion of light and wave motion in or fluids is general described as traveling waves.

The light given off by elements when they are heated in a flame (a movie showing a light bulb filament), the light from the sun, are all examples of radiant energy which is also called electromagnetic radiation. Electromagnetic radiation is composed of electric and magnetic components and exhibits wave properties (Wave Example file). In more general terms a wave is a continuously repeating change or oscillation of matter or a field in which the oscillation occurs. Light is thought to consist of an electric and a magnetic component, each at right angles to one another. Light exhibits wave character because it is bent when it enters a glass prism. When white light is focused on a prism it is separated into its component parts as each part is bent to a different angle as it passes through the prism.

So we need to have a clear understanding of waves. Waves are not unfamiliar to any of us, particularly if you have spent any time at the lake or swimming pool. Water exhibits characteristics of waves. A calm surface in a pool, lake or pond can be set into wave motion by a pebble or rock. Dropping the object into the water produces ripples (waves) emminating from the point of entry of the rock. We see these waves and we know they can transfer energy. If you have ever been hit by a wave you know it can transfer energy. But in our example of the lake, a leaf on the water surface near the point of entry can be set into motion when the waves make contact with it. So waves carry energy. We characterize waves using four important properties; wavelength, amplitude, frequency and velocity.

The animation (Wave Example file) shows a simple two dimensional representation of a wave. Although electromagnetic radiation is composed of magnetic and electric components, we will simplify this and only consider the electric component. According to our definition of a wave it is a continuously repeating change or oscillation of matter or a field. And we see how in this representation the wave is oscillating. Lets look at the four properties of a wave.

First is its wavelength (Physics WEB Site). The wavelength is the distance between repeating points on the wave and the symbol, is used. For light in the visible region the wavelength are very small and the unit used is the nanometer.

Amplitude is the distance between the highest (or lowest) point on a wave and the center of the wave. In the two waves shown, even though they have different wavelengths they have the same amplitudes. If we consider light in the visible region the amplitude controls the brightnest of light. The brighter the light the larger the amplitude of the wave.

Frequency is the number of waves which pass a point in space per unit time. The units of frequency are cycles per second (cps) or hertz (Hz) [named after Heinrich Hertz a pioneer in the study of electromagnetic radiation] and the symbol, is used. Dividing the number of waves passing the line by the time in seconds yields frequency. You should notice that the shorter the wavelength for the electromagnetic radiation the higher the frequency. The longer the wavelength the lower the freqency.

The velocity of a wave can be determined using the frequency, the number of waves passing a point per unit time, and wavelength, the distance between repeating points on the wave. If we know how many wave pass a particular point per unit time and we know the distance between the tops of the waves we can calculate the velocity. Expressing this relationship mathematically we have,

So if we know either the wavelength or the frequency for a sample of electromagnetic radiation we can calculate the other. For example,

From a macroscopic viewpoint nature appears to be continuous. If we go into the laboratory it is easy to measure 3.00 g of 24magnesium, 4.510 g of 24magnesium or any amount in between. On the atomic scale however, this is not the case.

An analog to the example of magnesium is the appearance of a sandy beach from a distance as a smooth, continuous surface. On closer inspection however, the sand consists of individual grains observable by the eye. If we look at our 3.00 g sample of 24magnesium more closely we see the individual atoms of 24magnesium each with a mass of 3.9822 x 10-22 g. We can not weigh out anything but whole numbers of atoms of 24Mg. Magnesium is not continous but comes in chunks called atoms.

In 1900 a total change in our view of matter occurred. One of the ideas which lead to this change was quantization. While the concept of a quantum was not new at this time it's application into new areas would result in some significant changes. We already have a feel for quantum, the atom is a quantum (bundle) of matter. Also atoms have integer numbers of electrons. We can not have atoms with 1/2 or 1/3 or 1/56 of an electron. Electrons exist as discrete bundles.

Atoms are considered quanta of matter.

In the late nineteenth century Max Planck and Albert Einstein realized that not only is matter quantized but energy and light could also be interpreted as quantized. While the details of Planck's pioneering work will not be discussed the results are important. Planck had to resort to such a description to explain experimental observations that he was collecting. Planck, as well as others, had noted that when a metal, or solid or a dense gas was heated they all behaved identically (here is a picture of a stove). They began by glowing red and as heat was added glowed white. Planck wondered why this occurred and set out to discover an answer. Planck studied the light emitted by an object being heated. He noted that as an object is heated it begins to glow giving off red light. If heating is continued such the object gets hotter and the color changes to orange and finally to white. Recall white is the color associated with the presence of all colors of light. As an object is heated it gives of red light first. Red light has the longest wavelength and shortest frequency of visible light. Since this is the color of light emitted when a small amount of energy is added to the object Planck associated low energy with small frequency. As the object is heated the energy of the light emitted increases and other colors are produced until all colors of light are produced and the object glows white.

Planck concluded that the energy gained or lost be an atom must be some integer multiple of the minimum energy an atom can give off. Planck argued that energy given off by an atom was proportional to the frequency of light the atom emitted,

To convert the proportionality to an equality Planck added an integer and a constant, now known as Planck's constant.

The integer n stands for the number of photons of light. Usually this value is 1, or it can be Avogadro's number (6.02 x 1023).

  1. Light is composed of photons, which are small, discrete bundles of energy. Planck imagined light as composed of a stream of particles called photons.

  2. The energy of a photon is proportional to its frequency;

In this equation h is called Planck's constant and has a value of 6.626 x 10-34 joule-seconds.

Example #1

A photon of orange light with a wavelength of 600 nm or 5.0 x 1014 sec-1 has an energy of;

Red light also consists of a stream of photons, however, the energy of this light is less than that of orange light because the frequency is of red light is less than orange light. The ideas were revolutionary, believe it or not. To suggest that light was composed of small bundles of energy.

From this relationship it is apparent that the size of the energy package, E, varies directly with the frequency of the radiation. High frequency light in the visible spectrum, which is violet, has the highest energy associated with it. Ultraviolet is even higher frequency and higher in energy. Red light has a lower frequency and also has lower energy. Recall that the frequency of one of the doublets in the sodium spectrum was 5.085 x 1014 sec-1. This frequency corresponds to light of this color (yellow) which comes in bundles of energy equal to 3.369 x 10-19 J. So light emitted from this line of the doublet of sodium contains photons (quanta of light) of energy equal to 3.369 x 10-19 J. If we have a higher concentration of sodium in the solution the light is more intense, or brighter, but the energy of the light does not change.

Einstein had to apply the Planck's idea of quantization of energy to understand the Photoelectric Effect, behavior of ejected electrons from a metal surface (orange lines) when light is shined on it. In the experiment Einstein observed that as the frequency of light, shining on a metal surface, is increased the energy of the electrons ejected from the metal also increased. (Demonstrating how light has particle properties) To explain the observations Einstein found the idea of considering light as small packets, or quanta, or massless particles helped him understand the effect. Einstein suggested that light was quantized and each individual quantum of light he called a photon.

However, there is a characteristic threshold which must be achieved before any electrons can be ejected. When we consider that light consists of photons, whose energy depends on its frequency, in order to remove an electron from the metal a certain minimum amount of energy must be acquired by the electron before it is ejected. This experiment suggests that the electrons that are around the atom, must absorb a certain amount of energy before they can leave their stable arrangement.

In the early 20th century scientists were troubled as to how atoms existed. According to classical arguments if the negatively charged electron revolved around the positively charged nucleus it would have to continuously loss energy, as electromagnetic radiation (light), and spiral into the nucleus. But the atom did not do this. In fact, as you recall, when atoms are placed in a bunsen burner we observed electromagnetic radiation being given off, not in a continuous way, but discretely, i.e. only certain lines are observed.

Two workers in 1859, Robert Bunsen and Gustav Kirchhoff, studied the light emitted by metals more closely using Bunsen's newly designed gas burner. He and Kirchhoff studied the light emitted by these metals by passing the light through a prism. The light split into its component parts, but it did not appear continuous, but as sharp lines. The sample tested by Bunsen and Kirchhoff emitted light of specific wavelengths or frequencies.

Emission spectra for elements.

Here is a site where the emmission spectra of most of the elements can be found. Since the light seemed to come form the elements the spectra where called emission spectra. The emission spectrum consists of colored lines on a dark background. The spectrum of an element is made up of spectral lines unique to that element. It was soon discovered that passing an electric current between electrodes sealed in a tube containing a vapor of an element in question yielded the same spectra.

These observations by Bunsen and Kirchhoff shed new light on another phenomenon called dark line spectra. When white light is passed through samples of metal vapor, dark lines appear in a continuous spectrum of the source. Careful measurement established that the missing lines were identical to the emission lines of Bunsen and Kirchhoff. The sodium vapor was absorbing the light. The conclusion: an element can absorb or emit light of a particular frequency, depending on the experiment.

The discrete nature of the emission spectrum of elements was surprising. However, it was not clear at the time the measurements were taken it was not taken too seriously. It was surprising, but why elements behaved in this manner was not immediately obvious. It wasn't until 1900 that these measurements became a part of a revolution in how scientists looked at the atom.

The hydrogen atom emission spectrum was very simple. When looking at the lines it was possible to derive a mathematical relationship that could reproduce the same pattern of lines as observed in the emission spectrum for the hydrogen atom. Other workers had looked at the emission spectrum for excited hydrogen atoms in the ultraviolet and the infrared regions and found the lines emitted by hydrogen atoms could be reproduced in either region with a slightly modified mathematical relationships. When looking at the emission spectrum for the hydrogen atom in all three regions a pattern can be identified.

The light produced by the atoms occurs at specific frequencies. Recalling Planck's relationship,

It is possible to calculate the energy of the photons emitted by an atom. So if the frequency of the photon emitted by an atom is large the energy lost by the atom is large, and visa-versa.

Niels Bohr, is credited with making the leap and determining the regularity associated with the hydrogen atom emission spectrum. Bohr combined classical physics with the quantum concept to derive a relationship which describes the energy of the hydrogen atom. Bohr recognized that Planck and Einstein's ideas of photons and discrete energy state could be applied to the discrete lines of the emission spectrum of hydrogen. Einstein had shown that electrons could be ejected from a metal atom if just enough energy could be supplied. Bohr assumed that the emission spectrum of hydrogen was due to the behavior of the electron in hydrogen. Bohr suggested the electron in a hydrogen atom could only have certain energies, otherwise the atom could emit light at all frequencies. In the flame the electron would absorb some energy and emit it at the same frequency.

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.

The important result for us which Bohr's model of atom provides is that the electron could only exist in certain allowed orbits. These orbits can also be called shells. When an electron absorbed the correct amount of energy it could be excited from one shell to another higher shell. The more energy the electron absorbed the higher the shell and the further the electron is from the nucleus. So if the electron absorbed the correct amount of energy it could be excited from the first shell to the second shell. That amount of energy was specific. If the amount of energy was a littlemore or a little less the electron would not be excited. Only the correct amount of energy could be absorbed. Bohr's model said that the energy required to excite an electron was quantized. Just as the distance each shell was from the nucleus.

However, there was a problem. Bohr's model could not explain the helium atom! Other chemists began looking at the problem. One of them, Schrodinger, found that when the electron was treated as a wave, not as a particle, something interesting was introduced. Schrodinger's results indicated that not only could the electron occupy a particlar level, but it could also occupy a particular sublevel in each level, and within each sublevel it could be in a particular orbital. This was getting very complicated. Yet the experimental evidence sggested that this could be the only way to think of the electron in an a wave.

The efforts by Schrodinger and others is as follows...the electron can be in any level, for example the first or second or third or even the fourth level. Each level contained at leastone sublevel. In fact, the number of sublevels possible in a particular level depended on the level the electron was in. If the electron was in the first level, it could only be in one sublevel. If it was in the second level, there were two possible sublevels the electron could occupy. If the electron was in the third level, there were three possible sublevels. The sublevel are given letter names like, s, p, d, or f. In the first level there is only one sublevel, the s sublevel. In the second level there are two sublevels, an s and a p. In the third level there are three sublevels, s, p, and d.

Finally each sublevel has a different number of orbitals the electron can be located in. Remember an orbital is a region of space (3D) where the probability of finding the electron is high. Any s sublevel contains a single orbital, a p sublevel contains three orbitals, and a d sublevel contains 5 orbitals.

So if an electron is in the first level it must be in the single orbital of the s subshell. If it is in the second level it could be in either an s or a p subshell. If it is in the s subshell in the second level it can only be in one orbital. If it is in the p subshell it could be in any of three possible orbitals.