Electromagnetic+Radiation

=**Electromagnetic Radiation**=

//from dvapphysics.wikispaces, the free AP Physics wiki that anyone in Mr. Adkin's class can edit////.//

Electromagnetic radiation, or electromagnetic waves, really only has three components to it for the AP test: knowing the properties of waves, recognizing the relationship between frequency and wavelength, and remembering the electromagnetic spectrum. toc

__Properties of Electromagnetic Waves__
The properties are really just memorization except with #3 and #4 there are equations to go with it. where E is the energy,// h //is plank's constant, ƒ is the frequency, λ is the wavelength, c is the speed of light,// p // is the momentum,// m // is the mass, and// v // is the velocity.
 * 1) Electromagnetic waves travel at the speed of light.
 * 2) Electromagnetic waves are transverse waves, because the electric and magnetic fields are perpendicular to the direction of propagation of the wave and to each other.
 * 3) The ratio of the electric field to the magnetic field in an electromagnetic wave equals the speed of light.
 * 4) Electromagnetic waves carry both energy and momentum, which can be delivered to a surface.
 * 1) 3 defines the equation: E/B=с
 * 2) 4 is based around the dual nature of light and the property of a photon rather than the wave of light itself and has the following equations:
 * Energy of a photon equation: E=// h //ƒ=// h //c/λ
 * Momentum of a photon equation:// p //=E/с =// h //c/(cλ) =// h/ //λ
 * de Broglie wavelength: λ=// h/p =h/(mv) //
 * Frequency of matter waves: ƒ=E/// h //

__Frequency vs Wavelength__
The relationship between frequency and wavelength is shown by the equation in which the speed of light is equal to the frequency multiplied by the wavelength, or с=ƒλ. The importance of this equation is to show that frequency and wavelength have an inverse relationship, as seen on the graph below.
 * Tip: this relationship will actually apply to more than just this section.*

__Electromagnetic Spectrum__
Now remembering the entire spectrum may seem difficult but they don't expect you to remember the EXACT numbers just the general ares. However, it it a must to remember the order of the spectrum. The picture shows gamma to x-ray to ultraviolet to violet, blue, green, yellow, orange, red to infrared, to micro, then to radio. Mr. Adkins teaches the opposite way, but either way is fine.

The picture seen on the above is a visual of the electromagnetic spectrum starting from the shortest wavelength, gamma rays, to the longest wavelength, radio waves.

These approximations were based solely off the relationship equation.
 * Gamma Rays**, having the smallest wavelengths of <1nm, have frequencies of about 10¹⁸Hz and greater.
 * X-rays**, having wavelengths of approximately 1nm, have frequencies of about 10¹⁷Hz.
 * Ultraviolet rays**, having wavelengths of about 100nm, have frequencies of about 10¹⁵Hz.
 * Visible light**, ranging from wavelengths of about 400nm to 700nm, have frequencies of about 10¹⁴Hz.
 * Infrared light**, having wavelengths of 800nm< λ <1mm, have frequencies of about 10¹²Hz< ƒ <10¹³Hz.
 * Microwaves**, having wavelengths of about 1mm, have frequencies of about 10¹¹Hz.
 * Radio waves**, having wavelengths of >1m, have frequencies of about 10⁸Hz and smaller.

Shown on the right is a graph showing the both the frequency and wavelength of the spectrum. Despite the slight off sets, both graphs as well as the approximations hold true to one another.

__Example Problems__
These questions may seem simple and honestly they are, but if you don't put the properties of waves, order of the spectrum, and the relation of wavelength to frequency into your memory bank for the test you will lose EASY points. Answers can be found following the problems, at the very end. Example 1: Which of the following types of radiation on the electromagnetic spectrum has the largest wavelength?

a) Gamma Rays b) Red Light c) Microwaves d) Radio Waves e) Ultraviolet Light

Example 2: Which of the following has the highest frequency in the electromagnetic spectrum?

a) Infared Light b) Red Light c) Yellow Light d) X-Rays e) Blue Light

Example 3: Which of the following has the smallest wavelength in the electromagnetic spectrum?

a) Blue Light b) Orange Light c) Yellow Light d) Red Light e) Green Light

Example 4: Which of the following has the lowest frequency compared to the others given?

a) Ultraviolet Light b) Gamma Rays c) Microwaves d) Visible Light e) Radio Waves

Example 5: Which of the following types of electromagnetic radiation possesses the most energy?

a) Red Light b) Blue Light c) Ultraviolet Light d) Infrared Light e) Gamma Rays

Example 6: Which of the following types of electromagnetic radiation possesses the least amount of energy?

a) Red Light b) Ultraviolet Light c) X-Rays d) Gamma Rays e) Orange Light

Example 7: A given electromagnetic wave has a wavelength of 400 nanometers. What is it's frequency?

Example 8: What is the de Broglie wavelength for a proton moving at 5m/s. a) 3.24x 10-⁸m b)7.94 x 10-⁸m c) 6.125 x 10-⁸m d)9.80x 10-⁸m e)1.54x 10-⁸m

__Answers__
These are the answers to the above examples:

1. (e), because radio waves exist on the lower end of the electromagnetic spectrum. Refer to the diagram in the explanations above.

2. (d), because according to the electromagnetic spectrum diagram shown above, X-Rays have the shortest wavelength out of the rest of the answers. Because frequency and wavelength are inversely proportional, the smaller the wavelength, the higher the frequency. Therefore X-Rays have the highest frequency out of the choices given.

3. (a), because of the visible lights, blue has the smallest wavelength out of the choices. This is still according to the same diagram mentioned above.

4. (e), because according to the diagram of the electromagnetic spectrum as shown above, Radio Waves have the longest wavelength out of the other choices. Also, because frequency and wavelength are inversely proportional, bigger wavelengths means lower frequencies.

5. (e), because Energy = (Planck's Constant) x (frequency). The higher the frequency, the higher the energy. Gamma Rays have the shortest wavelength and therefore the highest frequency.

6. (a), because Energy = (Planck's Constant) x (frequency). The lower the frequency, the lower the energy. Red Light has the longest wavelength and therefore the lowest frequency.

7. Answer: Step 1: 400 nm = 400 x 10 -9 m Step 2: с=ƒλ. f=c/λ. Step 3: f = (3 x 10 8 m/s)/(400 x 10 -9 m) = 7.5 x 10 14 Hz (cycles/second) Result: Frequency of the wave is 7.5 x 10 14 Hz. 8. (b), because the equation for this type of problem is λ= // h/mv //so you plug in v and although not stated directly the problem gives you m by saying it’s a proton and h is just plank’s constant. Mass of a proton is (1.67 x 10-²⁷kg), so what you do is plug and chug and you achieve the answer 7.94 x 10-⁸ m.

**Reference(s)**
All information was provided by: Serway, Raymond A (2006), //College Physics// (7th ed.): Brookscole ISBN 978-0-534-99723-6

Pictures were provided by various sites off Google (the pictures were checked to verify content): http://berkshireparanormal.com/uvexperiment.html http://swift.sonoma.edu/education/slinky_booklet/index.html http://wkp.maluke.com/en/Electromagnetic_spectrum http://www.astro.cornell.edu/academics/courses/astro201/wavelength.htm