# Energy levels

The diagram shows some of the energy levels of an electron in a mercury atom. Level Q represents the lowest possible energy level.

(a)Explain why a line spectrum results from an atom with such energy levels.

(b) Calculate the energy change in joules when the electron moves from level P to level Q and determine the wavelength of the spectral line associated with this transition.

(c)Explain what is likely to happen if a moving electron of energy 7.0eV collides with an isolated mercury atom in the ground state.

(d)Explain what is likely to happen if a photon, also of energy 7.0eV were to be incident on the atom.

Planck’s constant = 6.6 x 10-34 Js,
speed of light = 3.0 x 108m/s,
charge on an electron = 1.6 x 10 -19 C

Thanks in advance

## Answers and Replies

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I have at least tried to solve b)

-10,4 - (-5,5) = -4,9 eV = -7,84 * 10^-19J

f = E/h = (- 7.84 * 10^-19)/(6.63 * 10^-34) = - 1.18 * 10^15

lamba = (3 * 10^8)/(-1.18 * 10^15) = - 2.54 * 10^-7

Have I done something wrong?

Hootenanny
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Spruance said:
I have at least tried to solve b)

-10,4 - (-5,5) = -4,9 eV = -7,84 * 10^-19J

f = E/h = (- 7.84 * 10^-19)/(6.63 * 10^-34) = - 1.18 * 10^15

lamba = (3 * 10^8)/(-1.18 * 10^15) = - 2.54 * 10^-7
Nope, this looks correct to me.

~H

Hi

1) is not that important, I can always find some information on internet on it.

However, I didn't find any information in my textbook on c) and d). Anyone able (wanting? ...) to help me out?

Last edited:
Hootenanny
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Think in terms of 'if the electron / photon collides with an electron from a mercury nucleous'. With electron-electron collisions, the collision can either be elastic or inelastic. With a photon, all the energy is always absorbed by the electron. What happens if an electron gains energy?

~H

I'm not completely sure

Hootenanny
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Spruance said:
I'm not completely sure
Think about energy levels, excitation....

~H

I believe that the mercury atom would be excitated if it collides with a moving electron.

Hootenanny
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Spruance said:
I believe that the mercury atom would be excitated if it collides with a moving electron.
You would need to consider the energy of the electron, in relation to the energy levels of the mercury atom.

~H

I don't think the mercury atom would be ionized

Hootenanny
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Spruance said:
I don't think the mercury atom would be ionized
No it wouldn't, what I'm getting at is you should make reference to the energy of the electron / photon in your asnwer and compare it to the energy levels. Excitation is a key word you should use.

~H

10.4 - 7 = 3.4 eV

Hootenanny
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Spruance said:
10.4 - 7 = 3.4 eV
Correct, so it would be excited to the -3.7eV energy level.

~H

Thanks

What would then happen in d?

Hootenanny
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As, I stated previously;

Hootenanny said:
With a photon, all the energy is always absorbed by the electron. What happens if an electron gains energy?

~H