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An electron is in the second energy level (n=2) of a Hydrogen atom. What is the maximum wavelength of light that it can absorb and be completely ionized (removed from atom)? (Hint: The final state will be n = infinity)
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One way to do this is to first calculate the energy of the electron in the initial and final states using the equation:

En = (-13.6 eV)/n2

E2 = (-13.6 eV)/4 = -3.4 eV

E1 = (-13.6 eV)/1 = -13.6 eV

In dropping from the n = 2 state to the ground state the electron loses 10.2 eV worth of energy. This is the energy carried away by the photon.

Converting this to joules gives E = 10.2 * 1.60 x 10-19 J/eV = 1.632 x 10-18 J

For a photon E = hf = hc/l

l = hc/E = 6.63 x 10-34 * 3 x 108 / 1.632 x 10-18

l = 1.22 x 10-7 m = 122 nm
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