Practice Calculating Energy of Electromagnetic Waves

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  • 0:03 Electromagnetic Waves
  • 4:03 Photoelectric Effect
  • 5:55 Lesson Summary
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Lesson Transcript
Instructor: Matthew Bergstresser
Electromagnetic waves range from tiny gamma rays to large radio waves. In this lesson, we'll calculate the energy of various electromagnetic waves including how this applies to the photoelectric effect.

Electromagnetic Waves

If you are a fan of comic books and related cartoons, television shows, and movies, you are aware of a man that was accidentally exposed to gamma rays. Because of this exposure, he turns into a green monster when angered, which is a marvel! This may be a great story line, but gamma ray exposure leads to serious bodily damage, not superhuman powers.

Gamma rays have the most energy of all of the electromagnetic waves. Before we practice calculating how much energy gamma rays and other various electromagnetic waves possess, let's review the basics regarding electromagnetic radiation.

Electromagnetic Wave Generation

A vibrating electron generates an electromagnetic wave, which is two waves perpendicular to each other. One of the waves is an oscillating electric field, and the other is an oscillating magnetic field. The faster the electron vibrates, the smaller the wavelength (λ), but the velocity is always constant - the speed of light (3.0 x 108 m/s).


EM_wave

  • B is the oscillating magnetic field
  • E is the oscillating electric field
  • c is the speed of light
  • λ is the wavelength

Wavelength is the distance between successive peaks of the wave (crests) or between successive low points of the wave (troughs). Frequency is how many wavelengths pass a certain point per second. Wavelength and frequency have an inverse relationship: As one goes up, the other goes down.


EM_Eq1

Let's talk about the different types of electromagnetic waves. The electromagnetic spectrum is the range of electromagnetic waves ranging from the shortest wavelengths (gamma rays) to the longest wavelengths (radio waves).


EM_spec

A general rule to follow when determining the energy of electromagnetic waves is, the shorter the wavelength, the higher the energy it possesses.


E_eq

  • E is energy in joules (J)
  • h is Planck's constant (6.626 x 10-34 joule-seconds (Js))
  • f is frequency in hertz (Hz), which is 1/s

Let's practice using the energy equation to determine the energies of different electromagnetic radiations.

Example 1

Determine the energy associated with an x-ray whose frequency is 3 x 1017 hertz.

The frequency is given, so all we have to do is plug it in along with Planck's constant into the energy equation.


Ex1_eq1

Let's do another…

Example 2

How much energy is associated with a microwave whose frequency is 1.7 GHz?

To solve this, we use the same equation as before, but we need to convert GHz to Hz. The G represents the prefix giga, which is 109.


Ex2_math

One more…

Example 3

How much energy was associated with the gamma ray that struck our superhero character if the frequency was 1 x 1020 Hz?

Energy equation to the rescue:


Ex_3math

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