Group Activity: Light, the Electromagnetic Spectrum and Atoms

Light is also a photon: a particle with a definite ‘size’. That light is both a particle and a wave is a difficult idea and scientists have wrestled with the problem for centuries, at least since Isaac Newton wrote about light. In the early years of the twentieth century Albert Einstein and Max Planck showed some compelling reasons to think of light as a particle. In this activity we will deal with light in both ways. The ‘size’ of a photon is its energy. The energy of a photon is directly related to the fact that it is also a wave: its frequency. Fundamentally, light is a form of energy.

First, take a look at light as a wave. Waves, in general, are a vibrating disturbance by which energy is transferred. A familiar example might be the waves that you can make in water, say by throwing a pebble into a pond or by splashing in a swimming pool. Waves can also be invisible: sounds travel through the air as waves. Waves are described using three characteristics. Amplitude is how high a wave is; it’s the distance from the midline of the wave up to the top of a crest or down to the bottom of a trough. Wavelength is the distance between identical points on successive waves. Wavelengths are usually measured in meters. Both of these terms are illustrated at left. Frequency is the number of waves that pass by during 1 second (1 s). It’s the answer to the question, “how many per second?” and has the unit 1/s also called Hz after the radio pioneer Heinrich Hertz.

Light is a wave and so has frequency, wavelength and amplitude. The amplitude of light is related to the number of photons and it will not be of great concern here. Frequency and wavelength, however, are very important. In a vacuum (like outer space) light travels the highest velocity in the universe: c. The constant c is a fundamental constant of nature and is 3.00 × 10⁸ m/s. Every frequency of light has one and only one wavelength. Knowing the speed of light and the frequency makes it possible to calculate wavelength. Frequency can be calculated from the wavelength and the speed. This is possible because of the basic equation linking speed, wavelength and frequency of waves:

Speed Formula
c = λf
c = the speed of light, 3.00 × 10⁸ m/s
λ = the wavelength in meters (λ is the Greek letter lambda)
f = the frequency of light in Hz (1/s)

The units in this equation work out like this: (λ in m) × (f in 1/s) equal speed in m/s. [m × 1/s = m/s].

The energy of a wave of light is directly related to its frequency. Max Planck (1858 - 1947), the founder of quantum mechanics and the winner of the 1918 Nobel prize, found that light could only be emitted or absorbed in little packets. Planck called these packets quanta (singular: quantum); a quantum is the smallest quantity of energy that can be emitted or absorbed in the form of electromagnetic radiation (light). He discovered that the relationship between the energy of light and its frequency could be described by the following formula:

The units in this equation work out like this: (h in J· s) × (f in 1/s) equal energy in J. [J· s × 1/s = J]. The Joule (J) is a basic unit of energy. A 100 Watt light bulb used 100 J of energy for every second it is on.

Planck found that light could be emitted in whole number multiples of this quantum energy (hf, 2hf, 3hf, 4hf, etc.) but he was at a loss to explain why. Albert Einstein helped to resolve the mystery with a paper he published in 1905. He said in that paper that light is not just a wave but is also a particle. Each frequency of light has its own amount of energy and the energy emitted or absorbed comes in multiples of that energy because light comes in little packets called photons. A photon is a particle of light energy. One way to connect light-as-a-wave to light-as-a-particle is to think of the amplitude (the height of the wave) as representing how many photons there are. The higher the amplitude of the light wave, the more photons there are.

These two ideas—that light is a wave and a particle—can be put together in this way:

Remember: frequency is directly proportional to energy. That means that when frequency increases, so does energy. And when frequency decreases, so does energy. Notice how small a part of the spectrum is visible!

Light and the Atom

What does all of this have to do with atoms? Quite a lot, actually. The electrons in an atom occupy different shells called energy levels. The higher the shell of a particular electron, the higher the amount of electronic potential energy it has. When a boulder rolls down a hill or you drop your iPod the gravitational potential energy is changed into kinetic energy: the boulder rolls, the iPod speeds toward doom. When an electron loses electronic potential energy the energy is not changed into motion: it is changed into light.

Electrons lose electronic potential energy (or gain it) by moving from one shell to another like moving from one step to another on a staircase. If an electron is struck by a photon with a particular amount of energy it can be made to hop up to a higher shell. If an electron is in a higher shell it can spontaneously drop to a lower one. In the process it emits a photon with a particular amount of energy. Light is fundamentally a form of energy.These particular amounts of energy correspond exactly to the difference in the energy levels of the two shells. This is the reason why light energy is emitted and absorbed only in multiples of the quantum energy.

It may seem strange that atomic energy levels are quantized. That is, that they exist as a series of discrete steps with no fractional values allowed. But this is similar to some everyday things such as how chickens only lay whole numbers of eggs. Also, our cash money is quantized: it is based on the basic unit of a penny.

The structure of an atom should not be thought of as electrons orbiting the nucleus like planets around the sun. The ‘orbits’ shown in the picture on the left below are just meant to represent the different shells, or energy levels. It is probably better to draw the atom’s electrons in energy levels like in the picture to the right below. Electrons are normally found as close to the nucleus as they can fit in the available shells. To move up a level electrons must absorb a photon with the right amount of energy. To move down a level an electron must emit a photon with the right amount of energy.

These images borrowed from Jim Clark from his excellent page at http://www.chemguide.co.uk/atoms/ properties/orbitsorbitals.html

Constants of Nature
Speed of Light	c	3.00 × 10⁸ m/s
Planck’s Constant	h	6.626 × 10^-34 J· s
Important Formulas
c = λf (relates frequency and wavelength of light)
E = hf (relates energy of one photon and frequency of light)

Emitting and Absorbing Light

Atoms emit and absorb light. When they absorb light an electron moves from a lower energy level to a higher energy level. When they emit light an electron has moved from a higher energy level to a lower energy level. An excited state is when one or more electrons is in a higher energy level than it would be in the ground state. The ground state is the special condition in which all of the electrons in an atom are in the lowest possible energy level.

The first six energy levels of a hydrogen atom are shown at right. The potential energy an electron has in each level is shown in a table at left. The energies in the table are given in electron volts (eV). This is a special unit used in atomic physics and chemistry and it is valuable because it saves the user from a lot of very small numbers. One electron volt (eV) equals 1.602 × 10^-19 J. The energies are negative because they represent potential energy and when the electron is infinitely far away it has zero potential energy. As it gets closer to the nucleus the electron must lose energy (think of this as slowing down so it can be part of an atom). The energy values are negative because in order for the electron to get to that energy level it had to give up the amount of energy shown.

When an electron moves between energy levels it either absorbs or emits energy in the form of a single photon. The energy of the photon matches the difference in the energies of two energy levels that the electron transitions between. To find the difference in energies just find the absolute value of the difference: For example, say the electron transitions between level 5 and level 1. The difference in energies is then |-13.606 eV – (-0.544 eV)| = 13.062 eV. This must be converted to joules (J):

Using Planck’s Formula you can find the frequency of the photon that has this amount of energy.

The Speed Formula can be used to find the wavelength of this frequency of light:

The above examples can be run in reverse to find the energy change between two energy levels in an atom. In fact, that is really how scientists figure out the internal structure of the energy levels of atoms. Data are collected about what wavelengths of light are produced by atoms of an element in the form of an emission spectrum. The emission spectrum of an element is a unique signature for each element which shows the wavelengths of light emitted by the atoms when electrons in the atoms move from higher energy levels to lower energy levels. The spectrum of hydrogen atoms in the visible range is shown below. The lines you see are specific wavelengths of light that correspond to the energy changes from higher levels down to energy level 2.

Questions and Problems

Comprehension Questions

Answer the following questions using one or more complete sentences. Everyone in the group must write down complete answers. Discuss among your group members what the best way to answer the question is and then write it down. All members must write down the answer.

Define the following terms, use a drawing to help.
1. wavelength:
2. frequency:
3. amplitude:
What is light?
What is it about light that makes it a wave?
What is it about light that makes it a particle?
What is a Joule? Look it up and find out how many dietary calories it is equivalent to and report that value here.
What is meant by the ground state of an atom?
What is an excited state of an atom?
An electron must gain energy to move farther away from the nucleus. According to your reading what is the mechanism by which electrons gain energy to move to higher energy levels?
Just as a ball naturally rolls downhill (and not uphill) an electron naturally falls down to lower energy levels, eventually reaching the ground state. How is the excess energy released when this happens?
The amount of energy that can be absorbed or released by electrons is restricted to certain quantum values. Using this idea explain why atoms of an elements only absorb and emit light in specific wavelengths.

Mathematical Formulas

Here are the formulas important to this lesson solved for each variable that you will need to be able to find in this activity. Study them and learn how to rearrange the formula yourself to solve for each variable.

Planck’s Formula
Use the first to find energy in J from frequency in Hz.
           E   hf            E    
E = hf     - = --    so  f = -
           h   h             h
Use the second to find frequency in Hz from energy in J.
The letter h stands for Planck’s Constant and 
h = 6.626 × 10^-34 J·s

Speed Formula
           c   λf            c
c = λf     - = --    so  λ = -
           f   f             f
This is how to find wavelength in m from frequency in Hz.
The letter c stands for the speed of light and 
c = 3.00 × 10⁸ m/s

Speed Formula
           c   λf            c
c = λf     - = --    so  f = -
           λ   λ             λ
This is how to find frequency in Hz from wavelength in m.
The letter c stands for the speed of light and 
c = 3.00 × 10⁸ m/s

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Mathematical Problems

Use the Speed Formula to find wavelength (λ) given frequency or to find frequency (f) given wavelength. For each problem identify what part of the electromagnetic spectrum each problem refers to by using the spectrum on the second page of your packet..

f = 2.3 × 10¹⁷ Hz
λ = __________
f = 4.2 × 10¹⁵ Hz
λ = __________
f = 7.9 × 10¹² Hz
λ = __________
f = 6.5 × 10⁵ Hz
λ = __________

λ = 6.8 × 10^-11 m
f = __________
λ = 9.8 × 10^-5 m
f = __________
λ = 8.7 × 10¹ m
f = __________
λ = 1.03 × 10⁴ m
f = __________

Sometimes wavelengths of light are given in nanometers (nm, 1 m = 1 × 10⁹ nm) or micrometers (μm, 1 m = 1 × 10⁶ μm). Visible and ultraviolet light are measured using nanometers (nm) and infrared and some microwave wavelengths are are measured using micrometers (μm).

For each of the following problems find the wavelength in meters and then decide whether the light is in the UV/Vis range or the IR range. If it is in the UV/Vis range convert meters to nanometers. If it is in the IR range convert meters to micrometers.

f = 2.3 × 10¹⁵ Hz
λ = __________ m
λ = __________ nm or μm
f = 6.2 × 10¹⁴ Hz
λ = __________ m
λ = __________ nm or μm

f = 5.4 × 10¹² Hz
λ = __________ m
λ = __________ nm or μm
f = 3.1 × 10¹³ Hz
λ = __________ m
λ = __________ nm or μm

page break

Use Planck’s Formula to find energy (E) given frequency (f) or wavelength (λ) or to find frequency or wavelength given energy. For each problem identify what part of the electromagnetic spectrum each problem refers to by using the spectrum on the second page of your packet..

f = 2.7 × 10¹⁸ Hz
E = __________
f = 3.6 × 10¹⁴ Hz
E = __________
λ = 5.6 × 10^-10 m
E = __________
λ = 7.9 × 10^-4 m
E = __________

E = 1.49 × 10^-20 J
f = __________
E = 1.15 × 10^-27 J
f = __________
E = 4.82 × 10¹⁹ J
λ = __________
E = 1.32 × 10^-14 J
λ = __________

Calculate the energy in J of each of the lines in the hydrogen spectrum as shown on the last page of text you received with this packet (410 nm, 434 nm, 486 nm, and 667 nm). Use the wavelengths shown to find the frequency and use the frequency to find the energies of the photons responsible for each line. Report your results in a table on a separate piece of paper with the headings: Wavelength (nm), Wavelength (m), Frequency (Hz), Energy (J).
Convert the energies found in the previous problem into electron volts (eV).
Each line in an atomic emission spectrum represents the energy of a transition between two energy levels in an atom. What two energy levels in a hydrogen atom produce a photon with each of the wavelengths in the spectrum (410 nm, 434 nm, 486 nm, and 667 nm)? Hint: use the table defining the energy of each energy level to find differences that match the energy of each line in the spctrum.

An interim homework assignment idea: ask students to find λ for three
radio stations and come to class prepared to draw out the length on the board.
Next in the series for this activity: Light and Graphing the Relationship between Wavelength and Frequency and Graphing the Relationship between Energy and Frequency
The last page in this series is the Additional in-Class Problems page.
Here is the homework assignment that goes with this
group activity. Give this after all group activity pages have been completed.
Last updated: May 03, 2009 Home

Energy Level	Energy (eV)
6	-0.378
5	-0.544
4	-0.850
3	-1.512
2	-3.402
1	-13.606