Excited electrons and spectral lines

In summary, the problem states that there are two hydrogen atoms with excited electrons at the same energy level. The lifetimes of the excited electrons are t1 and t2. The question is which electron will have a wider spectral line when they emit photons during their descent. Using the equation E2-E1=-13.6(1/(N1)^2-1/(N2)^2) [EV], it is determined that the electron with the shorter lifetime will have a wider spectral line, as it descends directly to its original level. The electron with the longer lifetime will pass through several other energy levels before returning, resulting in several spectral lines. The uncertainty principle can also be used to prove this.
  • #1
berdan
32
0

Homework Statement



Well,the problem is such : There are two hydrogen atoms.In each atom electrons were excited to the same energy level.Lifetime of one of the excited electrons is t1,when lifetime of other is t2.

The question is : Which on of them had more wider spectral line,when during descend they emmited photons.


Homework Equations



The regular hv=E2-E1=-13.6(1/(N1)^2-1/(N2)^2) [EV]


The Attempt at a Solution



Well,I said that if one lifetime is bigger,then one of them descended directly to its original level (less time),and the one with bigger lifetime is the one that passed throught several other energy levels before returning to original.Thus,the one that passed throught several different orbits emmited several spectral lines ,when the one that returned "faster" to its original level has less "wider" spectral line.


I might be badly mistaken (in my assumption that longer "lifetime" means ,it passed throught several different orbits before returning back to its original).
 
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  • #2
Hello!

I think that the electron having a shorter lifetime would show wider spectral lines.

I think you have to change your approach towards the problem. Try to use the uncertainty principle to get your answer.
Do look at the proof that I have provided.

From the uncertainty principle,

ΔEΔt ~ [itex]\hbar[/itex] (considering E tto be ground state)
and
ΔE ~ hΔ[itex]\nu[/itex]
so,

Δ[itex]\nu[/itex] ~ 1/(2[itex]\pi[/itex]Δt)
This equation signifies that for a short lifetime the range of frequencies would be more, thus implying a wider spectral band.
 
  • #3
Well,I've just found the slide that talks about it,and you are absolutely correctous,sir.
He did used the uncertainty principles to get something close to this...Man,I never going to get this quantum stuff :(.

Thank you many many times.
 

1. What are excited electrons?

Excited electrons are electrons that have absorbed energy and have moved to a higher energy level within an atom. This can happen when the electrons are exposed to heat, light, or other forms of energy.

2. How do excited electrons produce spectral lines?

When excited electrons return to their original energy level, they release energy in the form of light. This light has a specific wavelength, which corresponds to a specific color. These wavelengths appear as spectral lines when we view the light through a prism or spectroscope.

3. What causes the different colors in spectral lines?

The different colors in spectral lines are a result of the different energy levels of the electrons within an atom. Each element has a unique set of energy levels, so the colors produced by excited electrons are also unique to that element.

4. Why do we use spectral lines in science?

Spectral lines are used in science because they provide valuable information about the composition and properties of elements. By analyzing the wavelengths of spectral lines, scientists can identify elements and determine their energy levels and other characteristics.

5. Can excited electrons be used in practical applications?

Yes, excited electrons have many practical applications. For example, they are used in fluorescent lights, lasers, and even in medical imaging techniques such as MRI. The different colors produced by excited electrons can also be used in chemistry and materials science to study the structure and behavior of molecules.

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