Hydrogen emission spectrum diagram

In summary: R [1/1^2 - 1/n^2] which is 1/1 = 1 x 1/n^2 and what not, forgot to change the formula back when i was posting... but I am not sure if that's even correct... i mean, especially for the other 2, what will the n prime be? i don't know what the n is... o:n and n' are the principal quantum numbers of those states between which the electron transition occurs, accompanied by photon emission. The energy of the photon is equal to the energy difference between the states. As energy is given, better to use the energy formula:
  • #1
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.
 
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  • #3
^ah, forgot about that, the first one it's = R [1/1^2 - 1/n^2] which is 1/1 = 1 x 1/n^2 and what not, forgot to change the formula back when i was posting...

but I am not sure if that's even correct... i mean, specially for the other 2, what will the n prime be? i don't know what the n is... o:
 
  • #4
n and n' are the principal quantum numbers of those states between which the electron transition occurs, accompanied by photon emission. The energy of the photon is equal to the energy difference between the states. As energy is given, better to use the energy formula

hv=13.6(1/n'2-1/n2)

The photon energies can be converted to wavelength with the formula λ = hc/E, and you will see that the highest energy corresponds to a photon in the Lyman series, in the UV range of the spectrum: It means electron transitions to the n'=1 level from the n=2, 3, 4 ... ones. Find out n with the Rydberg formula. The lowest energy photon is in the visible range and belongs to the Balmer series, where the electron jumps on the n'=2 level from the n=3, 4 ... levels. Determine n.

ehild
 
  • #5


I would suggest double-checking your calculations for the wavelengths and quantum numbers. It is important to be precise and accurate in scientific calculations. Additionally, I would recommend using a diagram or table to organize your information and make it easier to visualize the energy levels and transitions. You may also want to research or review the concept of energy levels and transitions in hydrogen atoms to better understand the relationship between energy levels and quantum numbers. Finally, make sure to label your diagram clearly and accurately. Good luck with your homework!
 

FAQ: Hydrogen emission spectrum diagram

What is a hydrogen emission spectrum diagram?

A hydrogen emission spectrum diagram is a visual representation of the wavelengths of light emitted by hydrogen gas when it is excited by an electric current or high temperatures. It shows the distinct lines of light that correspond to specific energy levels within the hydrogen atom.

Why is the hydrogen emission spectrum important?

The hydrogen emission spectrum is important because it provides valuable information about the energy levels and structure of the hydrogen atom. It also serves as a basis for understanding the emission spectra of other elements and for studying the properties of atoms and molecules.

How is the hydrogen emission spectrum produced?

The hydrogen emission spectrum is produced by exciting hydrogen gas with an electric current or high temperatures. This causes the electrons in the hydrogen atoms to jump to higher energy levels, and when they fall back to their original energy levels, they emit light at specific wavelengths, creating the distinct lines seen in the spectrum.

What do the different lines in the hydrogen emission spectrum represent?

The different lines in the hydrogen emission spectrum represent the energy transitions that occur within the hydrogen atom as electrons move from higher energy levels to lower energy levels. Each line corresponds to a specific change in energy level and therefore has a unique wavelength.

How is the hydrogen emission spectrum used in scientific research?

The hydrogen emission spectrum is used in scientific research to understand the energy levels and structure of atoms and molecules. It can also be used to identify elements and compounds and to study their properties. Additionally, the hydrogen emission spectrum is used in astronomical observations to identify the chemical composition of stars and other celestial bodies.

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