# 1251 HW 13 Question 9

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While in the first excited state, a hydrogen atom is illuminated by various wavelengths of light. What happens to the hydrogen atom when illuminated by each wavelength?

A) 656.5 nm?

B) 417.0 nm?

C) 314.2 nm?

Options Pick One:  stays in n=2 state, jumps to n=3 state, jumps to n=4 state, jumps to n=5 state, jumps to n=6 state, is ionized

For A- I found the answer to be jumps to n=3 by the equation 42.17 in the text because for hydrogen when the n initial=2 and the n final=3, lamda=656 nm

For B I cannot come up with the answer. Keeping with equation 42.17 and n initial=2 the values of the n final=4,5,6 do not produce values of lamda=417 or 314.2

For C- I found the answer to be is ionized but I'm not exactly sure why.

Is there another way of doing it, or am I missing something? What would cause  would cause it to remain at n=2 and what causes the ionization in part C? Thanks for your help.

edited Nov 30, 2014

For a bounded electron to get excited and move to an upper energy level, the energy of the photon has to match the energy difference between the levels.

In the case of B, the energy of the photon doesn't match the gap between n=2 and any upper levels. The photon energy is also not large enough to ionize the atom -- making the electron to escape the atom, which requires 3.401ev for n=2.  Therefore, nothing would happen and the electron will stay at n=2.

In C, the photon energy is 3.94 eV which is large enough to make the electron escape the atom and thus ionize the atom.

answered Nov 30, 2014 by (21,750 points)