Final answer:
Visible light photons, with an energy range of 1.63 to 3.26 eV, do not have enough energy to excite an electron in a hydrogen atom from the n = 1 to the n = 5 level. The transition requires 13.056 eV, which exceeds the energy provided by visible light.
Step-by-step explanation:
The student is asking whether a photon with a wavelength within the range of visible light (400 to 700 nm) has enough energy to excite an electron in a hydrogen atom from the n = 1 energy level to the n = 5 energy level. First, we need to consider the energy range of visible light photons, which is typically 1.63 to 3.26 electron volts (eV). The energy required for an electron transition within a hydrogen atom can be calculated using the energy levels specified by the Bohr model.
The energy for each level in a hydrogen atom is given by the formula En = -13.6 eV / n2, where 'n' is the principal quantum number of the energy level. To find the energy required for an electron to transition from n = 1 to n = 5, we would calculate the energy of level 1 and level 5 and then find the difference. This tells us the energy that a photon must have to induce this transition.
Using the formula: E1 = -13.6 eV, E5 = -13.6 eV / 52 = -13.6 eV / 25 = -0.544 eV. The difference in energy (ΔE) is E5 - E1 = -0.544 eV - (-13.6 eV) = 13.056 eV, which is considerably higher than the maximum energy of visible light photons (3.26 eV). Therefore, a photon of visible light does not have sufficient energy to excite an electron from the n = 1 to the n = 5 level in a hydrogen atom.