Wavelength (l), Frequency
(n) and Energy Calculations (E)

There are a few calculations you may perform that involve waves. Before I go
any further, you need to know the constants that are involved.

c=3.0 x 10^{8}m/s (the speed of light in a vacuum)

This constant "c" is how fast electromagnetic radiation (light for all
extensive purposes) travels. The other is "h", which called Planck's constant.

h=6.626 x 10^{-34} J s

This comes from the work of Max Planck preformed in 1900 using blackbody
radiation. There were discrete values of energy that differed by this constant.
In other words, all energy is a multiple of this constant multiplied by the
frequency of the wave of light. Energy is therefore quantized, it is always a
multiple of a single packet of energy.

Now on to the equations.

Wavelength (l)
and Frequency (n) Relationships

c=ln ,

where
l is wavelength in meters

n
is frequency in hertz, 1/s or s^{-1}

c=3.0 x 10^{8}m/s (the speed of light in a
vacuum)

Typical question #1- What is the
frequency of red light with a wavelength of 690.nm?
(1m=10^{9}nm)

First- l
is wavelength in meters, so convert nm to
meters

690.nm (

1m

)=6.90
x 10^{-7}m

10^{9}nm

Now we can rearrange the equation above and solve for frequency, since we
already know the constant, c.

n=c/l

n=

3.0
x 10^{8}m/s

=4.35 x 10^{14} s^{-1}

6.90 x 10^{-7}m

Typical question #2-
What is the wavelength of light in nm, that has a frequency of 6.6 x 10^{14}
Hz?

l=c/n

l=

3.0
x 10^{8}m/s

=4.55 x 10^{-7}m

6.6 x 10^{14} s^{-1}

convert m to nm

4.55 x 10^{-7}m(

10^{9}nm

)=455nm

1m

Energy (E) and Frequency (n)
Relationships- Energy is directly
proportional to frequency. To calculate energy from frequency (or vice Versa),
use the following equation

E=hn

where
E is Energy in Joules (J)

n
is frequency in hertz, 1/s or s^{-1}

h=6.626 x 10^{-34} J s

Typical Question #1- How much energy does
a photon of light with a frequency of 4.60 x 10^{14} s^{-1}
have?

E=hn

E=(6.626 x 10^{-34}Js)(4.60
x 10^{14} s^{-1})

E= 3.05 x 10^{-19}J

Energy (E) and
Wavelength (l)
Relationships- Since energy is
calculated from frequency, we can substitute for frequency
(n)
in the equation E=hn,
using n=c/l,
(from
c=ln).
Now we can do our
calculations in one step instead of 2. The new combined equation is:

E=hc/l

where
E is Energy in Joules (J)

l
is wavelength in meters

h=6.626 x 10^{-34} J s

c=3.0 x 10^{8}m/s (the speed of light in a
vacuum)

Typical Question #1- How much energy does
a photon of Red light with a wavelength of 690.nm? (1m=10^{9}nm)

First- l
is wavelength in meters, so convert nm to
meters