Ok so on an exam I am making corrections to my mistakes andthere is this questio

Question

Ok so on an exam I am making corrections to my mistakes andthere is this question If the Borh model is used, what wavelength of light would berequired for ionization of hyrdrogen? The answer is 636 nm, but I have no idea why. Please explain so I don't get this wrong again... :)Thanks Ok so on an exam I am making corrections to my mistakes andthere is this question If the Borh model is used, what wavelength of light would berequired for ionization of hyrdrogen? The answer is 636 nm, but I have no idea why. Please explain so I don't get this wrong again... :)Thanks

Explanation / Answer

I do not believe that 636 nm is the correct answer. Firstly, 636 nm is pretty much in the middle of the visibleregion and light and, as such, it does not have sufficient energyto ionize atoms.   The world would be a cruel anddifficult place if visible light ionized atoms in the air!!! Secondly, here's the calculation.   The n = 1 groundstate electron in an H atom is well known from Bohr theory to havean energy of -13.6 eV.   To ionize H, the electronmust be given an amount of energy equal to 13.6 eV to raise it upto E=0 where it is no longer bound to the nucleus.       E = h   f   =   h   c / (13.6 eV)(1.6E-19 J/eV) = (6.6E-34 J-s) (3E8 m/s) / cross-multiply and solve for wavelength to get final answerof   = 91 nm.    This very short wavelength is in the UV region and hassufficient energy to ionize H atoms.

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