The Hydrogen Spectrum?

Question

1) The energy of the electron in the lowest level of the hydrogen atom (n=1) is -2.179×10-18 J.
What is the energy of the electron in level n=5?

2) The electron in a hydrogen atom moves from level n=1 to level n=2. (a) Is a photon emitted or absorbed? (b) What is the wavelength of the photon?

3) An excited hydrogen atom emits a photon with a wavelength of 486.2 nm. (a) In what region of the spectrum is this photon? (b) What is the frequency of this photon?

4 A hydrogen atom in the ground state absorbs a photon of wavelength 97.2 nm. (a) What energy level does the electron reach? (b) This excited atom then emits a photon of wavelength 486.2 nm. What energy level does the electron fall to?

Answer 1

Read the textbook or visit wikipedia at:
http://en.wikipedia.org/wiki/Hydrogen_spectrum
http://en.wikipedia.org/wiki/Energy_level
etc.
You must study to learn anything.

Answer 2

1) Without considering the fine structure, the electron energy level of the hydrogen atom can be written as:
En = -2.179×10^-18 J/ n^2
Thus for n = 5:
E5 = -8.716x10^-20 J

2a) absorbed
2b) -2.179×10^-18 J*(1/4 - 1)
= 1.634×10^-18 J

3a) Visible
3b) ν = c/λ = (2.998x10^17nm/s)/ (486.2 nm)
= 6.167x10^14/s

4a) E = hν = hc/λ = (6.626x10^-34 Js)*(2.998x10^17nm/s)/ (97.2 nm)
= 2.044x10^-18 J
From -2.179×10^-18 J*(1/n^2 - 1) = 2.044x10^-18 J
n = 4
4b) E = hν = hc/λ = (6.626x10^-34 Js)*(2.998x10^17nm/s)/ (486.2 nm)
= 4.086x10^-19 J
From -2.179×10^-18 J*(1/n^2 - 1/16) = - 4.086x10^-19 J
n = sqrt(8) Wrong!! Are you sure the wavelength is 486.2 nm?

Answer 3

An electron can bypass to any variety of capability stages, and while it falls back off to a decrease point it supplies off capability as a photon, for this reason an emission line. this is the adaptation in capability stages that defines the frequency of an emission (E=hf), particularly than any property of the electron or variety of electrons --------------------------- n=4 -------------o-----o----- n=3 .............|.......| -------------o------------ n=2 .....................| .....................| -------------------o------ n=a million think of the circles interior the ideal line are electrons (interior the case of hydrogen this may well be 2 separate situations) the electron can fall to the two the line below, or 2 lines below, the capability hollow is diverse, so the photon given off can be diverse. In a hydrogen atom electrons falling to n=2 provide emission lines interior the Balmer sequence, electrons falling to the n=a million provide emission lines interior the Lyman sequence.