Waves, Quantum Theory, and Photons!

What is a wave?

A wave is a vibrating disturbance through which energy is transmitted. Waves are described by their height and length, which are measured by amplitude and frequency.

Wavelength - the length of the wave from peak to peak or trough to trough

Amplitude - the vertical distance from the middle of the wave to the peak or trough

Peak/Crest - top of the wave

Frequency - the number of waves that pass through one specific point

Trough - the bottom of the wave

The units of measurement for a wavelength vary. They can be measured in meters centimeters, nanometers, or Angstroms. An Angstrom is a unit of length equal to 10^-10 meters.

The Electromagnetic Spectrum:

Up until 1900, scientists believed that the energy of an electron acted like a wave, meaning it was able to move up and down. An example of this motion was found in electromagnetic (EM) radition. EM radiation is all around us and takes many forms. Most of the wavelengths and frequencies of EM radiation are invisible to the naked eye. Examples of common EM radiation are rays from the sun, flames from a burning fire, or x-rays.

The collection of all types of EM radiation is called the EM spectrum. The EM spectrum has seven different parts:

1. Radio

2. Microwave

3. Infrared

4. Visible

5. Ultraviolet

6. X-ray

7. Gamma Ray

The visible light spectrum from low to high energy can be memorized using...

Roger Makes Instruments: Violins, Ukuleles, Xylophone, and Guitars. (RMIVUXG)

Humans can only see one small part of the EM spectrum which is the visible spectrum. This rainbow-colored portion is made up of the colors that humans can see...

Red, orange, yellow, green, blue, indigo, violet (ROYGBIV).

The arrow and scale show that the color violet has a short wavelength and higher frequency, while the color red has a longer wavelength and a shorter frequency. ROYGBIV is displayed from longest to shortest wavelengths.

Sizes of Wavelengths in the Electromagnetic Spectrum...

Radio: can range from 1 meter and below (<= 1); about the size of a building

Microwave: can range from 1 to 10^-3; about the size of a grain of sugar

Infrared: can range from 10^-3 to 7*10^-7; about the size of a protozoan

Visible: can range from 7*10^-7 to 4*10^-7; about the size of a bacteria

Ultraviolet: can range from 3*10^-7 to 10^-8; about the size of a molecule

X-ray: can range from 10^8 to 10^-12; about the size of an atom

Gamma Ray: can range from 10^-12 and up (>= 10^-12); about the size of an atomic nuclei

A radio wave is long and wide, like a jump rope that is being waved up and down, while a gamma-ray is tiny, like the nucleus of an atom. The spectrum is displayed from widest to narrowest wavelengths.

Planck's Theory:

German physicist Max Planck discovered that electrons can also act like particles because when they hit a metal surface they emit electrons. Planck heated solids until they glowed red hot and then observed that they emitted Em radiation. He found that Em radiation was emitted in small packages. He called these packages quanta.

A quantum is the smallest quantity of energy that can be emitted or absorbed in the form of EM energy.

A simple explanation is that every day you deal with things in specific quantities. If you want to buy a candy bar, it costs 89 cents with a tax of 7%. You would owe $0.0623 or about 6 and one-fourth cents in tax, but you can't give someone one-fourth of a penny.

A quantum is like a penny. A penny is the smallest cash coin available in the US. You cannot give someone half of a penny. You also can't have any unit of energy smaller than a quantum.

What is a quantum worth?

Planck measured the energy of a quantum with this equation...

E = hv

Where h is Planck's constant at 6.626 & 10^-34 Joules (an SI unit of energy) and v is the frequency of the light absorbed or emitted.

Planck's constant relates the energy in 1 quantum of EM radiation to the frequency of that radiation. Or if you are using the speed of light, c, the equation for a quantum would be...

E = hc/a

Quantum theory is the study of matter and energy on the atomic and subatomic levels. Quantum theory allows scientists to understand how electrons behave and to make predictions. According to quantum theory, energy is always emitted in whole-number multiples of hv. For example, hv, 2 hv, 3 hv, but not 1.96 hv or 3.2 hv.

The Photon:

Albert Einstein was a German physicist who developed the theory of relativity. He was awarded the Nobel Prize in Physics in 1921 for his discovery of the Law of Photoelectric Effect. Albert Einstein took Planck's theory to the next level. Einstein shot a beam of light onto a metal surface which caused electrons to be emitted. This emission is called the photoelectric effect. Einstein found that the number of electrons that were ejected from the metal was proportional to the brightness of the light.

Photoelectric Effect - bright light = more electrons ejected

However, the energy of the light must be above a certain frequency (called the threshold frequency) for electrons to be ejected. If the energy is below the threshold frequency none of the electrons will be ejected.

In other words, electrons inside metal atoms are held together tightly so it takes a lot of light to push an electron out. If the light doesn't have enough oomph or isn't a high enough frequency it can't make the electron budge.

For example, imagine you are holding on to a basketball as tightly as you can with two hands. Another person wants to push the basketball out of your grip. That means that they must apply a lot of force to get you to let go o the ball. If they push at the ball lightly, you keep holding on to the basketball. But, if they push hard enough, they can knock it out of your hands. That basketball represents the electron. The hard push represents a beam of energy that is above the threshold frequency.

Einstein suggested that the beam of light that could eject an electron was a particle of light called a proton. He said that photons possess energy which is given by the equation...

E = hv

Energy is equal to the wavelength multiplied by the frequency of light absorbed or emitted.

So that means, a photon = a quantum

Photons are the smallest unit of energy (like a quantum) and have the following characteristics:

1. They are neutral and stable and have no mass.

2. They interact with electrons and have energy and speed that are dependent on their frequency.

3. They can travel at the speed of light, but only in a vacuum, such as space.

4. All light and EM energy are made of photons.