Hydrogen Emission Spectrum and Electron Energy Levels

[AN630078]

Homework Statement

Hello, below I have some questions concerning the energy levels of a hydrogen atom and its emission spectrum. I have attached the relevant diagrams from the question.

1.Which of the emission lines in the spectrum above does 486 nm correspond to?
2.In the emission spectrum of hydrogen there is no green line. How does the diagram of the energy levels help verify this?
Use calculations to support your answer.

Relevant Equations

E=hf

1. The 4th line from the left, being the aqua blue line, corresponds to a wavelength of 486 nm, as blue light has a wavelength in the range 450-495 nm.

2. This is where I am having the most difficulty, I have tried to answer the question comprehensively but I am not satisfied with my answer.
In the emission spectrum of hydrogen, visibly there is no green line. This is because when an electron falls down between two energy levels and leaves the excited state the energy is re-emitted in the form of a photon. The wavelength (or equivalently, frequency) of the photon is determined by the difference in energy between the two states.
Green light has a wavelength of 495-570 nm and a frequency of 526-606 THz.
The energy difference for green is in a range of;

E=h*f
E=6.63*10^-34*5.26*10^14Hz=3.38738*10^-19J
E=6.63*10^-34*6.06810^14Hz=4.01778*10^-19J

There is not a transition between the different electron energy levels of hydrogen corresponding to the energy required to emit a green line.

How can I improve upon this reasoning?

 

[PeroK]

You have a diagram with energies given in $eV$. And you have some energies given in joules. In my view, you haven't answered the question.

 

[kuruman]

To answer the question, you need to calculate the wavelengths corresponding to all the possible transitions in your energy level diagram and see which ones match the wavelengths of the colors that are given to you. You can limit the number of your calculations by noting that visible photons are in the range of no more than 4 eV or so.