What is the longest wavelength of light that can be absorbed by a hydrogen atom that is initially in the second excited state?
the longest wavelength (lowest energy) would be from the 2nd excited state to the 3rd excited state
To determine the longest wavelength of light that can be absorbed by a hydrogen atom in the second excited state, we need to first understand the energy levels of the hydrogen atom.
The energy levels in a hydrogen atom are determined by the Bohr model, which states that the energy of an electron in a hydrogen atom is given by the equation:
E = -13.6 eV / n^2
Where E is the energy level, -13.6 eV is the ionization energy of hydrogen, and n is the principal quantum number.
By using this equation, we can find the energy difference between the second excited state (n = 3) and higher energy levels. The energy difference between two levels can be calculated by subtracting the lower energy level from the higher one.
So, to find the energy difference between the n = 3 and n = ∞ levels, we have:
ΔE = E(∞) - E(3)
= -13.6 eV / ∞^2 - (-13.6 eV / 3^2)
= -13.6 eV
Now, we can convert this energy difference to the corresponding wavelength using the equation:
ΔE = hc / λ
Where ΔE is the energy difference, h is the Planck's constant (6.626 x 10^-34 J s), c is the speed of light (2.998 x 10^8 m/s), and λ is the wavelength.
Rearranging this equation, we can solve for λ:
λ = hc / ΔE
Plugging in the values:
λ = (6.626 x 10^-34 J s) * (2.998 x 10^8 m/s) / (13.6 eV)
λ ≈ 9.11 x 10^6 m
Therefore, the longest wavelength of light that can be absorbed by a hydrogen atom initially in the second excited state is approximately 9.11 x 10^6 meters.