Re: Does the principal quantum number, n, determine wavelength?

Hi Lauren

Wavelength is determined by the frequency and speed at which the 
disturbance propagates. In a vacuum, for light, that speed is c=300 
million metres/second.

To remove an electron from an atom requires the ionisation energy e=hf, 
so if we are to do this with an electromagnetic wave it must have 
wavelength shorter than c/f where f is given by the ionisation energy, e, 
divided by Planck’s constant h..

So your question is “Does the principal quantum number determine the 
ionisation energy e?”
The answer is yes.
But not ONLY the principal quantum number!
There are other ionisation states of single-electron removal, especially 
in metals like platinum (unfilled inner electron shells). It depends 
which electron you remove and how and where to. The energy of an electron 
in any given environment depends on all its quantum numbers.

The ionisation energy, e, is usually expressed in electron-volts (1 eV= 
23,053 calories per mole). 

To illustrate other things, in addition to principal quantum number, 
consider this experiment:
We shine light on a silver electrode in a vacuum two-electrode photocell.
 To have any chance to remove an electron the electric field of that 
light at the silver surface, must point in the right direction AND exceed 
a certain value. That surface is never smooth nor flat and in fact we 
know little of its microstructure. A few electrons will be so fortunately 
placed as to escape easily: others will collide on the way out with the 
many gas molecules still present in the highest vacua attainable.

So a good way to find the ionisation energy (work function) of silver is 
to find the negative voltage V, applied to the other electrode,  that is 
just enough to completely stop electrons leaving the silver. This is the 
Photoelectric work function e : it is the e which you need to calculate 
the wavelength.
There are electrons that will leave the silver because of their thermal 
energy (so there is another experiment where we measure the thermionic 
work function).

We find that for silver crystals the work function varies with crystal 
orientation and temperature:
Photoelectric e in volts 
3.67 (4)     4.1 to 4.75 (5)     4.26  (8)      4.5 to 4.52   (117)     
4.73 at 20 deg C for well outgassed polycrystalline silver (6)
4.56 at 600 deg C  for well outgassed polycrystalline silver (6)
4.74 from the (111) crystal face (9)
4.75 from the (111) crystal face (7)
4.64 from the (100) crystal face (8) 
4.81 from the (100) crystal face (7)
4.52 from the (110) crystal face (8)
Thermionic e in volts:
3.09 (1)      3.56 (2)        4.08 (3)    4.31 (115)

References:
(1)	Wehnelt & Seliger, Zeits. f. Physik 38, 443 (1926)
(2)	Ameiser, Zeits. f. Physik 69, 531 (1927)
(3)	Goetz, Zeits f. Physik 43, 531 (1927)
(4)	Lukirsky  & Prilesaev, Zeits f. Physik 49, 236 (1928)
(5)	Fowler, Phys Rev 38, 45 (1931)
(6)	Wineh, Phys Rev 37. 1269 (1931)
(7)	Farnnsworth & Winch, Phys Rev 58, 812 (1940)
(8) Dweydari & Mee, Phys Status Solidi A, 17,247 (1973)
(9) Eastament & Mee, J Phys F, 3, 1738 (1973)
(115) Mitchell & Mitchell, Proc Roy SocA210, 70(1952)
(117) Fainshtein, Zavodskaya Lab 14, 64 (1948)
 
Some ideas on the “true” – they mean theoretical – work function are 
discussed (differently) in:
Fomenko, Emission Properties of Materials, 3rd edition, Naukova Dumka, 
Kiev (1970)
Riviere, Solid State Surface Science, vol 1, Marcel Dekker, chapter 4 
(1969)
Trasatti, Chim Ind (Milan), 53 (6), 559 (1971)
Lang & Kohn, Phys Rev B, 3(4), 1215 (1971)

Solid surfaces are very interesting because we understand little of them. 
See Anisotropy,  Allotropy and surface chemistry in Google.

If you have further questions we will try to either answer them or at 
least tell you where to look to find out more.
David