Atomic Structure and Energy Levels

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Context

Scientists are constantly trying to model things that they can't see. The first real model of the atom was the raisin pudding (or plumb pudding) model. In 1907 Ernest Rutherford made new observations that were not consistent with the raisin pudding model and the solar system model was put forward as the atomic theory. New experiments, however, were not consistent with the solar system model and so it too had to be discarded.

What are atomic energy levels?

When speaking of atomic energy levels we are referring to the energy state of the electrons within the atom. It is thought that the electrons reside in energy states and the probability of finding an electron in specific areas around the nucleus is connected to the energy state of the electron.

Explanation

Before continuing we need to think about light. There are four main ways to identify light: color, wavelength, frequency, and energy. Color is only good for visible light and it is very subjective. Different people will attribute different colors to the same object. Red can be bright red, orange-red, etc. You may know of a way to remember the basic colors like ROYGBIV which means red, orange, yellow, green, blue, indigo, and violet. This is often associated with the colors of the rainbow. One way to think about wavelength is that it is the distance between the peaks of a wave. The frequency is the number of waves that go by per second. Visible light is only a small part of the electromagnetic spectrum. Infrared light, which we can't see, is responsible for the warmth we feel when standing in the sunlight. Ultraviolet light can't be seen either, but it is responsible for sunburns. Radio waves, microwaves, x-rays, and many others are also different kinds of "light". Each has a characteristic wavelength, frequency, and energy.

Energy is inversely proportional to wavelength (as the wavelength goes up the energy goes down) and directly proportional to frequency (as the frequency goes up the energy also goes up). Blue has a shorter wavelength than red and, therefore, a higher energy and higher frequency. ROYGBIV orders the visible colors from low energy to high energy. Light can be equivalently described by wavelength, frequency, or energy. If you know one of these three, you can calculate the other two. They are connected together. It is the energy description of light that we will focus on in this course.

Around the same time that Rutherford was doing the Gold Foil experiment another great scientist, Neils Bohr, was conducting experiments with atoms that looked at the different colors of light emitted by the atoms. An interesting aspect of his observations was that each element had a unique set of colors (or, better stated, energies) associated with it. This is used today to figure out what elements are in stars and other celestial bodies that we can't get direct samples from.

This section will help you:

• Better understand light.
• Describe what happens when light is given off by atoms.
• Understand the basis of the current atomic theory.

Model

Bohr attributed the unique set of colors that he observed to the energy of the electrons changing as they moved from one energy level to another one. Going from a higher energy to a lower energy level would release energy which could be in the form of light and that would be consistent with his observations. Also, it would be necessary to say that the energy levels were discrete and fixed for each element because only certain colors (energies) were observed and not a continuous range of colors is given off. Since the solar system model was the current model at that time Bohr was trying to explain his observations in the context of electrons orbiting around the nucleus like planets around the sun. To get discrete energy levels he said that each orbit corresponded to a specific energy and that there were only certain orbits available in an atom. The available orbits would be unique for each element and would result in a unique set of colors being given off by each element. This would allow him to explain his observations about light by saying that the electrons were moving from one discrete orbit to another discrete orbit and giving off light in the process.

His prediction that electrons reside in discrete energy states and that the electrons can move between these energy states is a major contribution to our understanding of atomic theory and is part of the current model. Electrons can move to higher energy states when excited. They can be excited by light, heat, electrical energy, etc. Electrons, like everything else, want to be in the lowest energy state. So, after they are excited by the light or other energy, they "fall" back down to the lower energy state. Conservation of energy requires that energy be given off when going from a high energy to a low energy. This energy is often given off as light. This accounts for Bohr's observations. Notice, however, that it isn't required that the electrons go around in orbits, they just need to have different discrete energy states available to them.

To bolster his theory, Bohr used the solar system model to mathematically model a hydrogen atom. He used hydrogen because it only has one proton and one electron in the neutral atom. His mathematical model perfectly matched his observations and it predicted other energies of light that were later found by experiment. On a roll, he tried to do the equations using the solar system model for lithium which has two protons and two electrons. Unfortunately he couldn't get it to work. Others tried to modify the equations to account for elliptical orbits (more like planets), but to no avail. In fact using the solar system model only works for hydrogen. This and other experiments within about 12 years forced them to conclude that the solar system model couldn't be correct and that it must be discarded just like the raisin pudding model before it. The current model retains some of the ideas and terminology of the original Bohr model, but it is probabilistic in nature and uses quantum mechanics to describe the atom. In quantum mechanics we can only predict where an electron is likely to be for a given energy level, we never know where the electron actually is.

Again, it is a curious finding from observing the light given off as electrons fall back to lower energy states that each element gives off characteristic energies of light. It is also found that each element only absorbs certain characteristic energies. Furthermore, the energies absorbed and the energies emitted are the same! This again leads to the conclusion that the energy levels are discrete, like steps on a ladder. The electrons can't be found between steps. The energies observed form a line spectrum. It is distinguished from a continuous spectrum (which has all possible colors) in that only certain colors are observed, with dark spaces in between.

The selective absorption of light by atoms and molecules gives rise to much of the color around us. The leaves are green because chlorophyll only absorbs the complement of green (when the complement of green is absorbed we see green). Neon signs, night sticks, glow in the dark toys, and fireworks give off their characteristic colors due to this quantum effect. The world would certainly be a boring place without quantum effects!

Thinking Questions

1. Why was the solar system model of the atom discarded?
2. How did Bohr's observations lead him to think atomic energy levels must be discrete?
3. Why is color not a good way of describing light?
4. Describe the basic components of Bohr's observations.
5. What are the three ways (other than color) to characterize light? How are they related to each other?