The energy of a photon required to move an electron from energy level 1 to energy level 6 can be calculated using the formula E = hf, where E is the energy of the photon, h is Planck's constant, and f is the frequency of the photon. The energy emitted when an electron moves back to a lower energy level is equal to the energy difference between the two levels. The black bars in the total absorption spectrum represent the wavelengths of light that are absorbed by the atom.
The energy of a photon can be calculated using the formula:
E = hf
Where E is the energy of the photon, h is Planck's constant (6.63 x 10^-34 J s), and f is the frequency of the photon.
To find the frequency required to move the electron from energy level 1 to energy level 6, we need to calculate the energy difference between the two levels.
ΔE = Efinal - Einitial = E6 - E1
ΔE = (-13.6 eV) - (-3.4 eV)
ΔE = -10.2 eV
To convert the energy to joules, we can use the conversion factor 1 eV = 1.602 x 10^-19 J:
ΔE = (-10.2 eV)(1.602 x 10^-19 J)
ΔE = -1.637 x 10^-18 J
Since the electron is moving to a higher energy level, energy needs to be added to the atom. Therefore, the energy of the photon required to move the electron to energy level 6 is 1.637 x 10^-18 J.
As for the rule regarding the energy needed to move an electron to a higher energy level compared to the energy emitted when the electron moves back to the lower energy level, the energy emitted will be equal to the energy difference between the two levels.
Interpreting the total absorption spectrum, the black bars represent the wavelengths of light that are absorbed by the atom when electrons move to higher energy levels.