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### 905-I: Photon Formulas 2

• Topic Cluster: Waves
• Topic: The Electromagnetic Spectrum: Quantitative
• Objective: Quantitatively relate wavelength, frequency, and photon energy of a wave; problems are asked in all directions in tabular form
• Content: Because the wavelength, frequency, and energy electromagnetic photons comprise such as wide range of magnitudes, rarely used metric units are frequently used to express them; these units must be properly converted before and after using any formula
• Level: 4

#### BACK to Ladder The Electromagnetic Spectrum: Quantitative

In a previous pod, you learned the formulas that relate the frequency, energy, and wavelength of a photon of light. In this pod, you will continue using those formulas. Two changes make this pod more difficult. Firstly, not all photons presented are visible light, so you have a much wider range of order of magnitudes to consider for each variable. Secondly, each individual step is not listed. You need to know, on your own, when to complete the requisite conversions, when to use which formula, and when to refer to each constant.

## Reference Information

#### Table of Electromagnetic Waves

Type of Wave
Wavelength
greater than 1 meter
Microwave
between 1 millimeter and 1 meter
Infrared Light
between 700 nanometers and 1 millimeter

Visible Light

Red
between 635 nanometers and 700 nanometers
Orange
between 590 nanometers and 635 nanometers
Yellow
between 560 nanometers and 590 nanometers
Green
between 520 nanometers and 560 nanometers
Blue
between 450 nanometers and 520 nanometers
Violet
between 400 nanometers and 450 nanometers
Ultraviolet Light
between 10 nanometers and 400 nanometers
X-ray
between 1 picometer and 10 nanometers
Gamma Ray
less than 1 picometer

#### Formulas

$$c = \lambda f$$

Symbol
Quantity
SI Unit
$$c$$
Speed of Light (3e8)
m/s
$$\lambda$$
wavelength
meters
$$f$$
frequency
Hertz (1/s)

Note that frequency is also sometimes denoted by the Greek letter nu: $$\nu$$.

$$E = h f$$

Symbol
Quantity
SI Unit
$$E$$
Energy of Photon
Joules (J)
$$h$$
Planck's Constant (6.626e-34)
Joule-seconds
$$f$$
frequency
Hertz (1/s)

#### Constants

• $$c = 3.00 \text{E}8$$ The speed of light is always 300,000,000 m/s.
• $$h = 6.626 \text{E} -34 \text{ J} \cdot \text{s}$$

#### SI units

• Wavelength
• The SI unit for wavelength is meters.
• You must convert wavelength to meters before using any formula.
• When solving any formula for wavelength, the you solution will be in meters.
• Frequency
• The SI unit for wavelength is Hertz.
• You must convert frequency to Hertz before using any formula.
• When solving any formula for frequency, the you solution will be in Hertz.
• Energy
• The SI unit for wavelength is Joules.
• You must convert energy to Joules before using any formula.
• When solving any formula for energy, the you solution will be in Joules.

## Problems

Each row contains one piece of information. From this one piece, determine the missing information. Record each item in the unit provided. Write all work, including formulas and conversion factors.

Problem
Type of Wave
Wavelength
Frequency
Photon Energy
Speed
1. 630.
nanometers
teraHertz
electron-volts
m/s
2. centimeters
500.
megahertz
micro-electron-volts
m/s
3. millimeters
80.0
gigaHertz
micro-electron-volts
m/s
4. 15.0
nanometers
petaHertz
electron-volts
m/s
5. picometers
petaHertz
200.
kilo-electron-volts
m/s
6. 420. nano
meters
teraHertz
electron-volts
m/s
7. micrometers
teraHertz
124
milli-electron-volts
m/s
8. Pick any FM radio station
meters
Between 87.5 and 108.0 megaHertz
nano-electron-volts
m/s
9. Pick any AM Radio station
meters
between 550 and 1720 kHz
nano-electron-volts
m/s
10. Highest energy gamma ray burst ever recorded
meters
Hertz
1 tera-electron-volt
m/s