Energy level jumps...?
Calculate the fequency of light emitted (for the first 3, and absorbed for the second 3) when each of the following energy transitions occurs in the hydrogen atom:
a) n=3 to n=2
b) n=4 to n=1
c) n=2 to n=1
a) n=3 to n=4
b) n=3 to n=6
c) n=3 to n=5
Even if you don't work them out just please tell me how to figure this out!!!
Answers & Comments
Verified answer
Use the Rydberg formula, which gives you the wave length for the jump from level n2 to level n1:
1/λ = RH · ( 1/(n1)² - 1/(n2)² )
RH = 1.0967758×10^7m^-1 is the Rydberg constant for hydrogen
Wavelength and frequency are related by:
ν = c/λ
c = 2.99792458×10^8m/s
Combine both equations to:
ν = ν₀ · ( 1/(n1)² - 1/(n2)² )
with ν₀ = c · RH = 3.28805×10^15Hz
For the first set of problems i get the following results.
a) ν = 0.4567×10^15Hz
b) ν = 3.0825×10^15Hz
c) ν = 2.4660×10^15Hz
In the second set of problems light is absorbed to raise the electron to a higher level. Because the energy difference of the is the same as for a jump in the reverse direction, the frequency of the light absorbed is the same as of the light emitted by reverse jump. Hence you can use the formula above.
a) ν = 0.1598×10^15Hz
b) ν = 0.2740×10^15Hz
c) ν = 0.2338×10^15Hz