Wavelength Range

[405996618]

For the 10th question on the second homework, we are asked to find the wavelength range in nanometers, whenever n=5. I found the number of spectral lines, but how do I find the the wavelength range?

[Marin_Rice_2D]

Hi!

In order to find the wavelength range you'll need to first use the equation v = R (1/n2^2 - 1/n1^2). If n=5 the shortest frequency will be from the change in energy levels from n=5 (n1) to n=1 (n2) and the longest will be between n=5 (n1) and n=4 (n2). Using the equation above solve for the frequency from both energy level changes. Once you solve for the frequencies you'll need to use the equation 'lambda' = c/v to find the wavelength range. Substitute the frequencies you got in the previous step into the new equation and you'll get the wavelength range. You'll then have to convert your answer from meters to nanometers which can be done by multiplying the answers by (10^9 nm / 1 m).

Hope this helps!