Help...Hard wavelength Equation?

Question

Calculate the wavelength of light emitted when each of the following transitions occur over the following in the hydrogen atom. What type of electromagnetic radiation is emitted in each transition?
a. n=3 →n=2
b. n=4→n=2
c. n=2→n=1

Calculate the maximum wavelength of light capable of removing an electronfor a hydrogen atom from the energy state characterized by n=1 and by n=2

Answer 1

I will solve (a) for you, and you can work on (b) and (c) yourself.

Without considering the fine structure, the electron energy level of the hydrogen atom can be written as:
En = -2.179×10^-18 J/ n^2
Thus for n = 3: E3 = -2.421x10^-19 J
For n = 2: E2 = -5.448x10^-19 J
The transition energy is: E3 - E2 = 3.026x10^-19 J

Now to convert energy (in J) to frequency or wavelength, please remember this formula:
E = hν = hc/λ
where E the energy in J, h the Plank constant 6.626x10^-34 J•s, ν the frequency in 1/s or Hz, c the speed of light 2.998x10^8 m/s, and λ the wavelength in m. Therefore:
λ = hc/E = (6.626x10^-34 J•s)*(2.998e8 m/s)/(3.026x10^-19 J)
= 6.565x10^-7 m = 656.5 nm (red)

For relationship between the wavelength and color, please refer to:
http://en.wikipedia.org/wiki/Visible_light
For the calculation of the maximum wavelength of light capable of removing an electronfor a hydrogen atom from the energy state characterized by n=1 and by n=2, you are asked for the lowest energy surficient to excite the electron from n=1 and from n=2 state, that is n=1 →n=2, and n=2 →n=3.