Final answer:
To calculate the maximum wavelength of light capable of removing an electron for a hydrogen atom from the energy state characterized by n = 1 and n = 7, use the relationship between energy level and wavelength, converting energy in eV to joules and applying E = hc/lambda to find the wavelength.
Step-by-step explanation:
The maximum wavelength of light capable of removing an electron for a hydrogen atom from the energy state characterized by n = 1 can be found using the formula for the energy levels of the hydrogen atom, En = -13.6 eV/n2 (where En is the energy of the nth level and n is the principal quantum number). The ionization energy or the energy required to remove the electron from the n = 1 state is 13.6 eV. To find the maximum wavelength, we use the relation E = hc/λ (where E is the energy in joules, h is the Planck's constant, c is the speed of light, and λ is the wavelength). To remove an electron from n = 7, we need to just overcome the energy holding the electron in that level, which is much less than at n = 1.
From n = 1, the maximum wavelength λmax can be found by converting the ionization energy from eV to joules (1 eV = 1.602 x 10-19 J), then using the formula for energy and wavelength:
λmax (n=1) = hc/E1
From n = 7, we calculate the energy difference between the n = 7 level and the point of ionization (essentially, the n = ∞ level). The maximum wavelength λmax would be:
λmax (n=7) = hc/(E∞ - E7)