If a laser has a wavelength of 429nm, what is the frequency of this radiation in megahertz?

Answer 1

When doing these types of problems, you should memorize the following relationships:

E = hv

E = hc/λ

c = λv

E = energy; h = Planks constant; c = speed of light; v = frequency; λ = wavelength

Then use the correct formula and the correct units and you'll be able to do all these problems.,

In the current problem we know λ (wavelength) and we want to find v (frequency)

Which formula do we use? We use c = λv

c = speed of light = 3x10⁸ m/sec

λ = wavelength = 429 nm but we want to use meters to be consistent with units in speed of light

429 nm x 1 m / 1x10⁹ nm = 429x10^-9 m = 4.29x10^-7 m

v = ? = c/λ

v = 3x10⁸ m/sec / 4.29x10^-7 m = 6.99x10¹⁴ sec^-1 = 6.99x10¹⁴ Hz

Since they ask for the answer in megahertz, we convert as follows:

6.99x10¹⁴ Hz x 1 MHz / 1x10⁶ Hz = 6.99x10⁸ MHz