In Chapter 6 we will explore some of the experimental evidence which has lead to our modern view of the electronic structrue of the atom.

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 to 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 (QuickTime movie or 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 (QuickTime movie or Shockwave file) shows the range and where visible light is located. Wave motion of light and wave motion in fluids is general described as traveling waves. There is another type of wave motion common to string instruments called standing or stantionary waves. This type of motion occurs when the ends of a string or wire are fixed and not allowed to move. Let's discuss their characteristics and look at the pattern they produce.

Here are three examples of standing waves;

Standing Wave #1

Standing Wave #2

Standing Wave #3

First you should note that the amplitude of the standing wave at the fixed ends is zero. At the fixed ends there is no motion. Looking at standing waves #2 and #3 do you see other points where there is no motion? In Standing Wave #2 the point midway between the peak and the valley does not move. This point, along with the fixed ends, is called a node.

So in Standing Wave #1 there are two nodes; in Standing Wave #2 there are three nodes; and in Standing Wave #3 there are four nodes.

In the Standing Wave #1 the distance between the ends of the string, a, is . In the Standing Wave #2 the string length is equals one wavelength, or 2.. In the Standing Wave #3 the string length is equal to 3/2 wavelengths, or 3.. If standing Wave #4 was shown the string length would contain 4. wavelengths. etc.

Could the distance between ends of the string ever be 3/4 of a wavelength, or 3/2.? No because the standing wave can only have certain allowed values, for which there are no intermediate values. Since the ends of the string are fixed the only allowed vibrations are those which where;

a = n.

where n is an integer with only whole number values.

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 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 integral 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. 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.

  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. 600 nm = 5.0 x 1014 sec-1 orange light has 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.

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 B and K 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 B and K. 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.

Bunsen and Kirchhoff had determined that the emission spectra consisted of discrete lines. Looking at one of the simplest emission spectra, that of hydrogen, several workers were able to empirically arrive at a relationship which reproduced the line spacings observed. A Swiss school teacher by the name of Joseph Balmer noted a pattern in the discrete lines in the visible region of the emission spectrum of hydrogen. Using the frequency of the lines Balmer empirically arrived at the following equation;

'n' can have values of 3, 4, 5, ........

At the same time other workers studied the emission spectrum of hydrogen in the ultraviolet and infrared region. A scientist by the name of Lyman found a similar arrangement of lines in the ultraviolet region. The equation Lyman suggested was

'n' can have values of 2, 3, 4, 5, ........

A third series, in the infrared region this time, was identified by a scientist named Paschen. The empirical relationship determined by Paschen was,

'n' can have values of 4, 5, 6 ........

Putting the three empirical equations next to each other the similarity is immediately evident. And so it was to Johannes Rydberg who noted each group of lines in the emission spectrum, independent of their location in the electromagnetic spectrum, could be correlated. First Rydberg noted that the first quotient was a simple square of a whole number. Then Rydberg generalized the equation suggesting variables for the first quotient and the second quotient.

'n' can have values of 1, 2, 3, 4, 5, 6 ........

Such a regular relationship for the hydrogen emission spectrum could not be coincidental and must suggest some regularity in behavior. 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.