Need a formula for Ionization HELP

[heliumhigh]

Need a formula for Ionization HELP!

What is the greatest wavelength of radiation that will ionize an unexcited Hydrogen atom?

If someone could give me a fomula to work with I'd be EVER so greatful! I've been working on this for HOURS.

 

[Tide]

The longest wavelength corresponds to the lowest photon energy which would have to be at least equal to the ground state energy of a hydrogen atom. It's possible (I haven't checked) that longer wavelengths could accomplish this as a multiphoton process using intermediate excited states but those states usually have VERY short lifetimes.

 

[kyle8921]

I understand your frustration and the importance of finding a formula for ionization. The formula for ionization is given by the Rydberg formula, which is 1/λ = R(1/n1^2 - 1/n2^2), where λ is the wavelength of radiation, R is the Rydberg constant (1.0974x10^7 m^-1), and n1 and n2 are the initial and final energy levels of the atom, respectively.

To find the greatest wavelength of radiation that will ionize an unexcited Hydrogen atom, we can set n2 = ∞ (since the atom is unexcited) and solve for n1. This gives us n1 = 2, meaning that the electron in the Hydrogen atom must be excited from the ground state (n1 = 1) to the first excited state (n2 = 2) in order to be ionized.

Substituting n1 = 2 and n2 = ∞ into the Rydberg formula, we get 1/λ = R(1/2^2 - 1/∞^2) = R/4. Rearranging, we get λ = 4/R = 3.03x10^-7 m, which is the greatest wavelength of radiation that will ionize an unexcited Hydrogen atom.

I hope this formula and explanation help you in your research. Remember to always double check your calculations and use reliable sources for information. Good luck!