The equation that relates wavelength, frequency, and speed of light is

#c = lambda*nu#

#c = 3.00xx10^8# #"m/s"# (the speed of light in a vacuum)

#lambda# = wavelength in meters

#nu# = frequency in Hertz (Hz) or #1/"s"# or #"s"^(-1)"#.

So basically the wavelength times the frequency of an electromagnetic wave equals the speed of light.

FYI, #lambda# is the Greek letter *lambda* , and #nu# is the Greek letter *nu* (it is not the same as a v).

To find wavelength (#lambda#), the equation is manipulated so that #lambda = c/nu#.

**EXAMPLE PROBLEM 1**

What is the wavelength of a electromagnetic wave that has a frequency of #4.95xx10^14# #"Hz"#?

**Given or Known:**

frequency or #nu = 4.95xx10^14# #"Hz"# or #4.50xx10^14# #"s"^(-1)"#

#c = 3.00xx10^8# #"m/s"#

**Unknown:**

Wavelength or #lambda#

**Equation:**

#c = lambda*nu#

**Solution:**

#lambda = c/nu = (3.00xx10^8"m"/color(red)cancel(color(black)("s")))/(4.95xx10^14color(red)cancel(color(black)("s"))^(-1)") = 6.06xx10^(-7)# #"m"#

*But what if you don't know the frequency? Can you still find the wavelength? Yes. An equation that relates energy and frequency is:*

#E = hnu#

#E# = energy in Joules #("J")#

#h# = Planck's constant = #6.626xx10^(-34)"J"*"s"#

#nu# = frequency = #"Hz"# or #"s"^(-1)"#

To find frequency, the equation is manipulated so that

#nu = E/h#

Once you have frequency, you can use the first equation #c = lambda*nu# to find the wavelength.

**EXAMPLE PROBLEM 2**

What is the wavelength of an electromagnetic wave having #3.28 xx10^(-19)# #"J"# of energy?

**Given or Known:**

#E = 3.28xx10^(-19)# #"J"#

#h = 6.626xx10^(-34)# #"J"*"s"#

**Unknown:**

frequency, #nu#

**Equation:**

#E = hnu#

**Solution: Part 1**

#nu = E/h = (3.28xx10^(-19)color(red)cancel(color(black)("J")))/(6.626xx10^(-34)color(red)cancel(color(black)("J"))*"s") = 4.95 xx10^14# #"Hz"# or #4.95xx10^14# #"s"^(-1)#

**Solution: Part 2**

#lambda = c/nu = (3.00xx10^8"m"/color(red)cancel(color(black)("s")))/(4.95xx10^14color(red)cancel(color(black)("s"))^(-1)") = 6.06xx10^(-7)# #"m"#