Number of Wavelengths from Excited H Atom (n=9)

In summary, if a hydrogen atom's electron is excited to the n = 9 level and loses energy, there can be a total of 36 wavelengths of light emitted. However, the number of distinct "hops" the electron can take is much smaller and can be quickly enumerated.
  • #1
Pengwuino
Gold Member
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Assume that a hydrogen atom's electron has been excited to the n = 9 level. How many wavelengths of light can be emitted as this excited atom loses energy?

Theres the question presented to me.

Now in all my wonderful glory, I enter "8" and boom, I am wrong. Just to be sure... i do 6, 7, 8, 9, and 10. None of them work. Then i start thinking... ok it can transfer from n=9 to n=8 to n=3 to n=1... but then that brings up an incredible number of combonations.

Am I right here with 8 or have i lost all comprehension of the H atom?
 
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  • #2
You're right, there's a lot of combinations of "hops" the electron can take in going from n = 9 down to n = 1. But the number of distinct, individual "hops" is actually fairly small. You should be able to enumerate them quickly.
 
  • #3
So shouldn't it be roughly a 8+7+6+5+4+3+2+1 deal?
 
  • #4
If I correctly understand the question, you can get the number of wavelengths by:
[tex] n_{wavelengths} = \frac{n_{level} (n_{level} -1)}{2} [/tex]
 

Related to Number of Wavelengths from Excited H Atom (n=9)

1. What is the significance of the excited state n=9 in hydrogen atoms?

The excited state n=9 in hydrogen atoms represents the ninth energy level or shell that an electron can occupy. This means that the electron in the hydrogen atom has absorbed enough energy to jump from its ground state (n=1) to the ninth energy level (n=9).

2. How many wavelengths can be emitted from an excited hydrogen atom in n=9 state?

The number of wavelengths that can be emitted from an excited hydrogen atom in the n=9 state depends on the specific electron transitions that occur. For n=9 state, there are a total of 36 possible transitions, resulting in 36 possible wavelengths.

3. Can the excited state n=9 in hydrogen atoms be observed in nature?

Yes, the excited state n=9 in hydrogen atoms can be observed in nature. However, it is a highly unstable state and the electron will quickly return to its ground state by emitting a photon. This emission of a photon is what we observe as a spectral line.

4. How does the number of wavelengths emitted from an excited hydrogen atom change as the value of n increases?

As the value of n increases, the number of possible electron transitions and wavelengths emitted from an excited hydrogen atom also increases. This is because the energy difference between energy levels decreases as n increases, allowing for more possible transitions.

5. What is the relationship between the number of wavelengths and the energy of an excited hydrogen atom in the n=9 state?

The number of wavelengths emitted from an excited hydrogen atom in the n=9 state is directly proportional to the energy of the atom. As the energy of the atom increases, the number of possible transitions and wavelengths also increases.

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