1. Electrons as Waves

2. Characteristics of Waves
Wavelength
The shortest distance between equivalent points on a continuous wave; either crest to crest or trough to trough
Measured in m

3. Characteristics of Waves
Frequency
the number of waves that pass a given point per second; one hertz (Hz) equals one wave per second

4. Characteristics of Waves
Amplitude
The wave's height from the origin to crest or origin to trough
Measured in m

5. The Wave

6. As shown in the formula, if wavelength increases, frequency decreases
As shown in the formula, if wavelength increases, frequency decreases. As wavelength decreases, frequency increases.

7. Electromagnetic Wave Relationship
speed = λ υ
c = speed of light
= 3.00 x 108 m/s

8. Sample Problem
If a gamma ray traveling at the speed of light has a frequency of 2.88 x 1021Hz, what is its wavelength?
speed = λ υ
3.00 x 108 m/s = λ (2.88 x 1021 Hz)
Answer: λ = 1.04 x m

9. Energy Energy will increase as frequency increases E = h υ
h is a constant = x Js

10. Sample Problem
A photon has an energy of 2.93 x J. What is its frequency?
E = h υ
2.93 x J = (6.626x10-34 Js) υ
Answer: υ = 4.42 x 105 Hz or 442,000 Hz

11. What about in this one?
What is the energy of an ultraviolet photon that has a wavelength of 1.18 x 10-8m?
E = h υ
But wait? Do we have frequency? No? So…Find it!
Speed = c = λ υ
3.00 x 108m/s = (1.18 x 10-8m) υ
υ = 2.54 x 1016
Now solve for the energy
E = (6.626 x Js) (2.54 x 1016)
E = 1.68 x J