## Waveswavelength, frequency, energy, speed

### parts of a wave

Wavelength: the distance between successive crests/peaks of a wave

Frequency: the number of waves that pass a fixed place in a given amount of time. Since we are measuring frequency in Hertz, we define frequency as the number of waves that pass a point in 1 second.

Period: Measured in seconds, the amount of time it takes for the wave to complete one full cycle. Period = 1 / frequency

#### E = h * f

E = Energy (measured in Joules)

h = Planck's Constant (always 6.626 x 10^-34, which will be given to you on the test)

f = frequency (measured in Hertz)

#### f = v / λͅ

f = frequency (measured in Hertz)

v = velocity/speed of the wave (**NOTE: Most of the time, the velocity of your wave is c, the speed of light. This number will be given to you on the test. The speed is equal to c if you are dealing with any form of electromagnetic radiation, and electron, or a photon.)

λͅ = wavelength (measured in meters) (**NOTE: If you are given wavelength in nanometers, you need to convert to meters before doing any calculations. There are 1 x 10^9 nanometers in 1 meter)

#### Moving energy levels in a Hydrogen Atom

Electrons in a hydrogen atoms jump from energy levels (labeled n = 1, 2, 3, . . .)

If you encounter a problem where you are told to calculate the energy of an electron moving from one level to another level, you will use this formula (which will be given to you on the test)

You will then use this formula twice -- plugging in the energy levels into the "n" variable

Example: One of the colors of light associated with the atomic spectrum of hydrogen is produced by the photon released when an electron drops from n = 5 to n = 2. Find the energy contained by one of these photons

Then you will take the energy from the final level and subtract the energy from the initial level:

This gives you the energy of the photon. You could then calculate the frequency by using E = h * f (you just got E, h is just planck's constant, so you can solve for f)

You could then get wavelength by using f = v / λͅ (you just solved for f with the last equation, v is velocity and you know that photons travel at the speed of light which will be given to you, so you can solve for wavelength)

#### A lot of these math problems will require you to use both equations: E = h * f and f = v / λͅ

You may have to use one one of the equations first to solve for a value, and then plug that value into the next equation.

#### Practice:

1) Calculate the energy of one photon of yellow light that has a wavelength of 589nm.

2) How much energy does a photon of light with a frequency of 4.60 x 10^14 Hz have?

3) What is the wavelength of light that has a frequency of 6.6 x 10^14 Hz?

1) E = 3.37 x 10^-19 Joules

2) E= 3.05 x 10^-19 Joules

3) 4.55 x 10^-7 meters