Energy levels and line spectra

Discussion in 'Chemistry' started by cnidocyte, Jul 9, 2010.

1. cnidocyteRegistered Senior Member

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15
I read that each line on a line spectra for an element represents an energy level. Hydrogen only has 1 electron which is in the first energy level so why are there so many lines on the H line spectrum?

3. rpennerFully WiredStaff Member

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4,833
Line spectra represent differences between energy levels.
Hydrogen has 1 electron, but that electron doesn't always spend its time in the ground (n=1) energy level.

$\Delta E \propto \frac{1}{n^2} - \frac{1}{m^2} \quad ( m,n \in {\bb N}_{+}, \, m \neq n )$

This pattern of lines was hard to figure out but is strong evidence that atomic hydrogen can only exist at discrete energy levels.

5. cnidocyteRegistered Senior Member

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15
So lets say I excite hydrogen and disperse the light through a prism and observe 4 lines. Does that mean the electron jumped up more than 4 energy levels?

7. rpennerFully WiredStaff Member

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4,833
If you excite atomic hydrogen you are putting the electrons of those atoms into non-ground states (2,3,4,5,6,7,....)
Then, a fraction of a second later, the electrons fall to various lower states.

If the new state (n) is 1, then the light is ultraviolet, and the electron is now in the ground state.
If the original state (m) is 7 or higher, and the new state (n) is 2, then the light is also ultraviolet.
If the original state is 3 to 6 and the new state is 2, then the light is visible.
If the new state is 3 or higher, then the first light is infrared, but then the electron can fall again and emit more light.

(6->2) 410.2 nm (violet) #5E00DB
(5->2) 434.1 nm (violet) #6A00FF
(4->2) 486.1 nm (bluish green) #0083B1
(3->2) 656.3 nm (red) #FF0000

If you see all of these lines, then at least some of the electrons went at least from 1 to 6, which is 5 energy levels.

http://en.wikipedia.org/wiki/Balmer_series
http://www.wolframalpha.com/input/?i=#5E00DB #6A00FF #0083B1 #FF0000

8. AlphaNumericFully ionizedModerator

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6,697
It gets more complicated when you include magnetic fields. When you apply an external magnetic field you can get a single 'normal' energy level emission line to split into multiple lines. Its known as Zeeman splitting and played an important role in people figuring out the properties of the electron, as it means the electron has some kind of quantised interaction with the magnetic field.

Rpenner has explained the 'normal' energy splittings very well. If you're competent at calculus (2nd year uni-ish) then you can have a look at the solutions to the Schrödinger equation, which provide the formal description of the electron orbitals in atomic Hydrogen, which are of the form of Legendre polynomials. The inclusion of magnetic fields basically generalised the polynomials to the associated Legendre polynomials.

That might be a little too mathematical but it forms the core of any kind of quantum mechanical analysis of the atom so worth a look perhaps.

9. TrippyALEA IACTA ESTStaff Member

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10,890
Because each series of lines in the spectrum of Hydrogen represents a many to one correspondence, and because you're dealing with a bulk sample of many gas atoms, rather than a single atom.

Consider, for example, the Lyman Series. The Lyman series represents the photon emissions produced by a bulk sample of gas when the electrons in transition from energy levels above the ground states, to the ground state. So the first line in the Lyman series represents the energy released by an electron transitioning from the 1st excited state to the ground state.
The second line represents the energy released when transitioning from the second excited state to the ground state, and so on and so forth.
Then we have the Balmer series, which represents transitions from higher levels, to the first excited state. The first line in the Balmer series represents the transition from the second excited state of hydrogen to the first excited state. and so on, and so forth.
Then we also have the Paschen Series, which is transitions to the second excited state, the Brackett Series which is transitions to the Third excited state, the Pfund series, which is transitions to the Third excited state, and the Humphrey's series which is transitions to the fourth excited state.

No.
What it means is that some electrons jumped up 4 energy levels, some jumped up 3 energy levels, some jumped 2 energy levels, and some only jumped one.

10. flora66Registered Member

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1
I just want to say thank you for the information.
It is very valuable for me..newbie here and encountering the same situation.
Thanks and keep up the good work..