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Wize University Chemistry Textbook > Early Atomic Theory to Quantum Theory

Electromagnetic Radiation

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Electromagnetic Spectrum

Up until this point in history, scientists were unsure if light shared the properties of waves or particles...there was some evidence for both!
The discovery of the electromagnetic spectrum showed the different wavelengths and frequencies that electromagnetic radiation could exist at. Since the different types of radiation in this spectrum behave as waves, and visible light is a part of this spectrum, it became clear to scientists that light acts as waves!


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Types of Electromagnetic Radiation

Photo by Rice University/ CC BY

  • In the diagram above, the electromagnetic radiation is organized from the types of radiation that are highest in energy (gamma rays) to the types of radiation that are lowest in energy (radiowaves)
  • You might recognize a lot of common household objects on the side of the spectrum with lower amounts of energy!


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Photon Equations

Electromagnetic Radiation Waves

  • Light (or electromagnetic radiation) behaves as a wave
  • A wave is a self-propagating transverse oscillation of electric and magnetic fields

where E is the electric field and B is the magnetic field
  • To describe waves, we can use the following terms:
  • Amplitude (A): the height of a wave crest or depth of a trough
  • Wavelength (λ): The distance a wave travels in one cycle (m)
  • Frequency (v): cycles per second (s-1 or units Hz)
  • Energy (E): units are Joules (J)

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Energy of a Photon Equations

E=hcλ=hv\boxed{E=\frac{hc}{\lambda}=hv}

where h is Planck's constant: 6.626x10-34 Js
and c is the speed of light: 3.0 x108 m/s



Wize Tip
You should memorize the value for the speed of light (c) = 3.0x108m/s as that value is not always provided on exams.


Wize Concept
Where will I see this on an exam?

Questions on this topic tend to arise in the form of a calculation. You will be asked to determine the energy or wavelength of a given ray of light.

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Photon Equations (Cntd.)

Key Relationships Between Variables in Photon Equations


E=hcλE=\frac{hc}{\lambda }
  • Are the E and λ of a photon directly or inversely proportional?
    inversely
    proportional


E=hvE=hv
  • Are the E and v of a photon directly or inversely proportional?
    directly
    proportional


hcλ=hv\frac{hc}{\lambda }=hv
  • Are the wavelength and frequency of a photon directly or inversely proportional?
    inversely
    proportional

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Summary


Photo by Rice University/ CC BY


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Example: Calculating Energy of a Photon Given Wavelength

A photon of light was found to emit light at 723 nm. How much energy is associated with this light?
h=6.626x10-34 Js

Wavelength and energy are related through this equation:

E=hcλE= \frac{hc}{\lambda }

We have Planck's constant (h) and know that the speed of light is 3x108m/s
The wavelength (λ) =723 nm

First, we must convert 723 nm to m.

723 nm x\frac{ }{ }1 m1 x 109 nm\frac{1\ m}{1\ x\ 10^9\ nm}= 7.23 x10-7 m

We can now plug in our values and solve for E:

E = 6.626 x 10−34 Js ⋅ 3.00 x 108 ms7.23 x 10−7 m\frac{6.626\ x\ 10^{-34}\ Js\ \cdot\ 3.00\ x\ 10^8\ \frac{m}{s}}{7.23\ x\ 10^{-7}\ m}

E = 2.75 x 10-19 J
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Watch Out!
Don't forget that for the photon equations E must in joules (J) and λ (wavelength) must be in m (meters) not nm (nanometers)!
  • If you are given a wavelength value in nm, you would have to convert it to m before plugging it into an equation.
Remember: 1nm=1x10-9m

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Example: Calculating Frequency of a Photon Given Energy

Calculate the frequency of a photon with an energy of 236 kJ.
h=6.626x10-34 Js
The following equation has both E and frequency (v) in it. Rearrange to solve for v:

E = hv  →  v = EhE\ =\ hv\ \ \rightarrow\ \ v\ =\ \frac{E}{h}

E must be in joules. Right now it is in kJ, so we must convert kJ to J:

236 kJ ⋅ 1000 J1 kJ = 236,000 J236\ kJ\ \cdot\ \frac{1000\ J}{1\ kJ}\ =\ 236,000\ J
Now we can plug in all values and solve for v:

v = 236,000 J6.626 x 10−34 J⋅s = 3.56 x 1038 s−1v\ =\ \frac{236,000\ J}{6.626\ x\ 10^{-34}\ J\cdot s}\ =\ 3.56\ x\ 10^{38}\ s^{-1}


Practice: Different Types of Electromagnetic Radiation

Rank the following types of electromagnetic radiation from lowest to highest energy.

Radio Waves, Infrared Radiation, X-rays, Microwaves, Visible Light, UV Radiation

Practice: Calculating Frequency of a Photon Given Wavelength

A photon of light has a wavelength of 700 nm. What is its frequency?
Extra Practice
Electromagnetic Radiation
A green laser pointer emits light at 532.0 nm. What is the frequency of this radiation?
Electromagnetic Radiation: Photon energy
A laser emits light at a wavelength of 710 nm.
What is the energy of a single photon from this laser?
Electromagnetic radiation: Wave energy
A laser emits light at a wavelength of 710 nm.
What is the frequency of this light?
Photon
What is the energy of a light wave with frequency of 1.04×1015Hz1.04\times10^{15}Hz?
Electromagnetic Radiation
As the wavelength of light decreases, which is also true of light?
Energy of Light
A UV light of frequency 2.73 ⋅\cdot 1016 s−1 is ____ times _____ in energy than a yellow light of frequency 5.26 ⋅\cdot 1014 s−1
Electromagnetic radiation
Which of the following wavelengths corresponds to a photon in the infrared region of
the electromagnetic spectrum?
Electromagnetic Radiation
If a photon of light has λ=478 nm,\lambda=478\ nm, what is it’s wavelength in meters?
Electromagnetic Radiation
A green laser pointer emits light at 532.0 nm. What is the frequency of this radiation?
Electromagnetic Radiation
Which of the following statements are true?
i. When an electron falls to a lower energy level in an atom, it emits electromagnetic radiation.
ii. The energy of electromagnetic radiation is directly proportional to its frequency.
Electromagnetic radiation: Frequency of light
Your mean professor (in a different course) shines a red laser pointer into your eye with a wavelength of 666 nm. What is the frequency of this light?
Electromagnetic Radiation: Photon energy
A laser emits light at a wavelength of 710 nm.
What is the energy of a single photon from this laser?
A laser emits light at a wavelength of 710 nm.
What color is the laser?
Laser Emitting Photons Problem
A laser emits a light beam with a power of 5 mW. The wavelength of the light is 374 nm. How many photons per second does this laser emit? (3mW=3mJ/s) Hint: Calculate the energy of a single photon
Power=5mW (light beam) based on conversion provided I know this is equal to 5mJ/s
wavelength=374nm -> convert to m: 1nm=1x10-9m, so 374x10-9m
Wavelength
Which of the following has the longest wavelength?
Electromagnetic Radiation
4. Rank the following from longest wavelength to shortest wavlength: Microwaves, ultraviolet, infrared, visible light, and X-rays. (In the table, 1=longest and 5=shortest)
Electromagnetic Radiation
An organic molecule absorbs radiation that has a frequency of 2.8 x 1015 s-1.
a) What is the wavelength of radiation?
b) What is the energy of radiation?
Electromagnetic Radiation
6. A carbon-nitrogen bond in an organic molecule absorbs radiation that has a frequency of 4.3 x 1012 s-1.
a) What is the wavelength of radiation?
b) What is the energy of radiation?
Electromagnetic Radiation
5. Which of the following statements are true?
Electromagnetic radiation: Wave Energy
Calculate the energy of one photon whose wavelength is 589 nm.
Practice: Photon
What is the energy of a light wave with frequency of 1.04×1015Hz1.04\times10^{15}Hz?
Electromagnetic Radiation
What is the wavelength of a photon of light, which has a frequency of 2.8 x 1014 Hz?
A photon of light has a wavelength of 700 nm. What is its frequency?
Electromagnetic radiation: Wave energy
A laser emits light at a wavelength of 710 nm.
What is the frequency of this light?
If a light wave has a wavelength of 420 nm, what is it’s frequency?
If the answer has an exponent write it like this 1.23x10^4 (no spaces)
Electromagnetic Radiation: Practice
Rank the following types of electromagnetic radiation from lowest to highest energy.
Radio Waves, Infrared Radiation, X-rays, Microwaves, Visible Light, UV Radiation
Transverse Waves
Use the graph below to answer the following questions:
1. Which wave has the lowest energy?
D
2. What is the wavelength of wave A?
200nm
Choose one of the following statements which is FALSE
An electromegnetic wave undergoes three complete oscillations over a 360 nm segment of space. What is the frequency of this wave?
Electromagnetic Radiation
Rank the following types of electromagnetic radiation from lowest to highest energy.
Radio Waves, Infrared Radiation, X-rays, Microwaves, Visible Light, UV Radiation
Electromagnetic Radiation: Energy
A photon has wavelength of 2.0 cm in space. What is its energy?
Electromagnetic Radiation: Energy of Blue Laser Pointers
An argon ion laser produces a blue laser beam with a wavelength of 458 nm. What is the energy of this light expressed in kJ/mol?
What is the wavelength of a an electromagnetic wave with a frequency of 3.78 x 1015 s-1?