Ionization energy is defined as the minimum energy required to remove an electron from the ground state (n0) to infinity (n∞). Determine the wavelength of radiation required to ionize the hydrogen electron from the n = 2 energy level. Calculate the energy (Joules) associated with this photon. (1 cm-1 = 1.986 x 10-23 J)

Question

do I use E = -RH / n^2 ?

I don't know why I'm given the cm to J conversion, or why they ask for the wavelength first.

Answer 1

I would do it the other way around.
delta E = 2.180 x 10^-18 J*[(1/n1^2)-(1/n2^2)]. With the Balmer series, n1 is 2 and n2 is infinity.
Then delta E = hc/wavelength.
The reason reciprocal cm is given (cm^-1) is because wave number = 1/wavelength and many spectroscopists prefer to use wave number instead of wavelength. Also, if you use the Rydberg constant, then
1/wavelength = R[(1/N1^2) - (1/N2^2)] and you don't need to convert to wavelength first to get energy in joules.

Answer 2

ok so 1/lambda = (2.18e-19) (.25 - 0)
1/lambda = 5.45e-19

then i set up a proportion to convert it into joules?

1 cm-1/1.986e-23 joules = 5.45e-19 cm-1/x

I got x = 1.082e-41 joules and that it so not right..

Answer 3

thank you i got it now!!

thanks so much for your help!!