The yellow light given off by a sodium vapor lamp has a wavelength of 589nm. What is the frequency of this radiation? Please show all work.

5.09 x 10⁶ s⁻¹ = 5.09 x 10⁶ Hz

Explanation:

The relation between frequency (ν) and wavelength (λ) is given by:

λ = c/ν

where c is the speed of light (2.998 m/s) and it is a constant.

So, we first convert the wavelength from nanometers (nm) to meters (m) (1 nm = 1 x 10⁻⁹):

λ= 589 nm x (10⁻⁹ nm/1 m) = 5.89 x 10⁻⁷ m

Then, we calculate the frequency from the equation:

λ = c/ν ⇒ ν = c/λ = (2.998 m/s)/(5.89 x 10⁻⁷ m) = 5.09 x 10⁶s⁻¹ = 5.09 x 10⁶ Hz