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iym185

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## Homework Statement

Hydrogen atom with ionisation energy 13.6 eV is found to have an emission spectrum with lines at 1.89 eV, 10.20 eV and 12.09 eV. Draw a labelled diagram to show the energy levels of hydrogen atom by showing the transitions of electrons causing the emission of the lines stated. Label also the quantum number of the corresponding energy levels in your diagram.

## Homework Equations

E = hc/λ ---> λ = hc/E

and

1/λ = RH [1 - 1/n^2]

## The Attempt at a Solution

alright, now i understand how to draw an energy diagram, I am just having trouble with this question:

thus far, i think I've correctly gotten to what the 'λ'are for this diagram:

using equation: E = hc/λ ---> λ = hc/E

1) 13.6 --> 1.89 = 1.8736x10^-18 J

λ = (6.626x10^-34)(3x10^8) divided by 1.8736x10^-18

λ = 106.095nm (Lyman Series)

2) 13.6 --> 10.2 = 5.44x10^-19

λ = (6.626x10^-34)(3x10^8) divided by 5.44x10^-19

λ = 365.4 nm (Balmer Series)

3) 13.6 ---> 12.09 = 2.416x10^-19

λ = (6.626x10^-34)(3x10^8) divided by 2.416x10^-19

λ = 822.76 nm (paschen series)

alright, assuming those are correct, I am now having trouble finding the quantum numbers 'n'... i made an attempt:

using : 1/λ = RH [1 - 1/n^2]

__Lyman__

1/(106.095x10^-9) = 1.097x10^7 [1 - 1/n^2]

n = 1.89

and i did that for the other 2:

Balmer: n=43.59

Paschen: n =56.25

buuut, now i don't really get what next... or if the n is correct... as i know, the 'n' in an energy diagram, has got to be whole number starting 2,3,4,5... so I am not sure what now... i mean, i get how to draw the diagram, i just don't know what the quantum numbers are... which the question is asking me to find.