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# Electromagnetic Waves

### Skills to develop

• Explain what electromagnetic waves are
• Calculate frequencies and wavelengths of light
• Explain Planck's hypothesis of photons or quanta
• Explain Einstein's photoelectric experiment
• Calculate photon energy, E = h v (read as h nu)

# Electromagnetic Waves

Transmission of energy through a vacuum or using no medium is accomplished by electromagnetic waves, caused by the osscilation of electric and magnetic fields. They move at a constant speed of 3x108 m/s. Often, they are called electromagnetic radiation, light, or photons.

Did you ever wonder what is electromagnetic radiation? The word is somewhat complicated, but you are in contact with electromagnetic radiation all the time. Here is a diagram of the electromagnetic radiation spectrum that has appeared in many text books and websites. Electromagnetic radiation is caused by the disturbance of an electromagnetic field.

The last line of numbers in power of 10 gives the wavelength in m. The regions sometimes do not have a clear cut, because there is considerable overlap. For example, radio waves and microwaves bondary is very vague, but public regulation for their application (usage) is strict.

Electromagnetic waves are used to transmit long/short/FM wavelength radio waves, and TV/telephone/wireless signals or energies. They are also responsible for transmiting energy in the form of microwaves, infrared radiation (IR), visible light (VIS), ultraviolet light (UV), X-rays, and gamma rays. Each region of this spectrum plays an important part in our lives, and in the business involving communication technology. The list given above are in increasing frequency (or decreasing wavelength) order. Here again is the list of regions and the approximate wavelengths in them. For simplicity, we choose to give only the magnitudes of frequencies. That is we give log (frequency) (log(f)).

```
Region: Radio, FM,  TV, microwave, IR, VIS, UV, X-rays, Gamma rays.
Wavelength: 600 m  20 m   1 mc  1 mm 0.1 mm    1e-9 m    1e-12 m   1e-15 m
log (f): 6   7   8   9 10  11   12   13  14  15    20      23
```

Electromagnetic radiations are usually treated as wave motions. The electronic and magnetic fields oscillate in directions perpendicular to each other and to the direction of motion of the wave.

The wavelength, the frequency, and the speed of light obey the following relationship:

wavelength * frequency = speed of light.

The speed of light is usually represented by c, the wavelength by the lower case Greek letter lambda, l and the frequency by lower case Greek letter nu n. In these symbols, the above formula is:

l n = c

The electromagnetic radiation is the fundation for radar, which is used for guidance and remote sensing for the study of the planet Earth.

### The Visible Spectrum

Wavelengths of the visible region of the spectrum range from 700 nm for red light to 400 nm for violet light.

```    red 700 nm
orange 630
yellow 550
green 500
blue 450
violet 400
```
There is no need to memorize these numbers, but knowing that the visible region has such a narrow range of 400-700 nm is handy at times when referring to certain light.

### Photons - bundles of electromagnetic energy

In his research on the radiation from a hot (black) body, Max. Planck made a simple proposal. He suggested that light consists of photons. The energy, E, of each individual photon of a monochromatic light wave, is proportional to the frequency, n, of the light:

E = h n where h (= 6.626*10-34 J s) is now known as the Planck constant. Often, we write h = 6.626e-34 J s for simplicity.

For the convenience of your future study of electromagnetic radiation, you might want to know the units often used for it.

1 Hz = 1, hertz: cycle per second, for frequency
1 nm = 1E-9 m, nanometer: for wavelength of IR, visible, UV and X-rays.
1 pm = 1E-12 m, picometer: for X-rays and gamma rasy.

### The Photoelectric Effect

When photons shines on a metal plate, they free electrons. Energy is required to pull the electrons out of the metal surface, and this amount of energy is calle threshold. The excess energy of the photon appear as the kinetic energy of the electrons. Here is a simulation of the photoelectric effect, which gives a slightly different perspective. A photoelectric effect demonstration is also fun for you if you have the time.

Einstein learned of Planck's proposal, and he wanted to perform experiments to show if the proposal is true. At that time, the photoelectric effect was known, and he measured the kinetic energy of electrons released by photons. He did find a linear relationship between the kinetic energy of the electrons and the frequency of light used, (see diagram below).

Furthermore, he found the light of minimum frequency needed to release electrons from a metal to be constant, and this energy must be overcome in order to take the electron out of the metal. This energy is called the threshold energy, W. The formula to descirbe photoelectron kinetic energy Ek is

Ek = h v - W and the proportional constant is what is known as the Planck Constant. The minimum frequency is called threshold frequency. The quantity h v is the energy of the photon. In other words, the energy of the photon is completely given to the electron: h v = Ek + W Energy is conserved, neither created, nor destroyed. This formula also illustrates the (great) principle of conservation of energy.

### Confidence Building Questions

• What is the speed of light?

Discussion:
The limiting speed is 3e8 m/s. Nothing moves faster than the speed of light, which is 800 million (0.8 billion) meters per second.

• Radiation with a frequency 1e14 Hz is in what region of the electromagnetic spectrum?
a. ultraviolet
b. violet
c. yellow
d. red
e. infrared

Discussion:
Ultraviolet light has higher frequencies than violet light has. UV light has frequency greater than 8E14 Hz, IR frequencies are less than 4e14 Hz. Thus, radiation with frequency of 1e14 is in the IR region. (3E8 m/s)/(400E-9 m) = 8E14 Hz; (3E8 m/s)/(720E-9 m) = 4E14 Hz Visiable light are in the 4E14 to 8E14 Hz region.

• A typical yellow light has a wavelength of 550 nm. Calculate the corresponging frequency. (speed of light 3.0E8 m/s)

Discussion:
The visible radiation range lies between 8E14 and 4E14 Hz. Yellow light lies in the middle of the visible radiation range.

• The visible radiation zone are between 8E14 and 4E14 Hz. A typical X-ray has a frequency of 3E19 Hz. Calculate its wavelength in picometer, pm. (1 pm = 1E-12 m)

Discussion:
X-rays wavelengths are 3 orders of magnitude shorter than those of visible light.

• Calculate the photon energy of yellow light whose wavelength is 550 nm. (h = 6.626E-34 J s)

Discussion:
E = h c / wavelength
This corresponds to 2.18E8 J or 2.18E5 kJ per mole of photons. A mole of photons is called an einstein.

• The photon with minimum frequency that disloge an electron from Ag surface has 7.58e-19 J. Calculate its frequency. (h = 6.626E-34 J s)

Discussion:
The minimum frequency is called threshold frequency.

• The photon with minimum frequency of 1.14e15 /s disloge an electron from Ag surface. Calculate its wavelength in nm. (c = 3e8 m/s)

Discussion:
lambda = c/v = 2.62e-7 m or 262 nm. Minimum freuency imply longest wavelength. The light is in the UV region.

• The kinetic energy of photons from Ag surface by 150 nm photons is 6.6e-19 J. Calculate the threshold energy. (h = 6.626E-34 J s)

Discussion:
E = h v. Make sure you've got the right unit.