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Photon calculation Bohr model Chemistry HELP?
does a photon of visible light ( lambda ≈ 400 to 700 nm ) have sufficient energy to excite an electron in a hydrogen atom from the :
n=1 to the n=5 energy state?
from the n=2 to the n=6 energy state?
Please don`t just write down the answer, i have no idea how to do this equation. Thanks!
We can use Rydberg's formula to find the (maximum) wavelength w of a photon
needed to excite an electron from a lower energy level L to an upper level U.
The formula is: 1/w = R(1/L² - 1/U²) where w is the wavelength, L and U are the
lower & upper energy levels, and R is Rydberg's constant, experimentally found
to be 10967758 waves per meter for hydrogen.
For the first example: L = 1 and U = 5, so we have 1/w = 10967758(1-1/25) or
1/w = 10967758(0.96) = 10529047. Then w = 1/10529047 = 9.4975 * 10**-8 meter
or 94.975 nm, which is ultraviolet light. Visible light doesn't have enough energy.
For the second, L = 2 and U = 6, so 1/w = 10967758(¼ - 1/36) = 2437279
Then w = 1/2437279 = 4.103 * 10**-7 meters, or 410.3 nm, which is violet light.
So visible light in the violet end (410.3 nm. or shorter) will have enough energy
to raise an electron from the 2nd to the 6th energy state.
Whew again! Hope this helps!
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