Final answer:
The energy required to shift an electron from the first to the fifth Bohr orbit of a hydrogen atom is calculated using the Bohr model formula, and the wavelength of light emitted when the electron returns to the ground state is determined by the Rydberg formula relating energy transition to wavelength.
Step-by-step explanation:
To calculate the energy required to shift an electron from the first to the fifth Bohr orbit in a hydrogen atom, you can use the Bohr model formula:
E = -13.6 eV * (1/n12 - 1/n22), where n1 is the initial orbit and n2 is the final orbit.
Substituting n1=1 and n2=5 into the formula, we calculate the energy required. For the wavelength of the light emitted when the electron returns to the ground state, we use the Rydberg formula that relates the energy transition to the wavelength: λ = hc/ΔE, where λ is the wavelength, h is Planck's constant, c is the speed of light, and ΔE is the energy difference between the two states. To find the wavelength of the specific transition, one must calculate the energy difference between the fifth and first orbit and then apply the energy to the wavelength formula.
The emission would result in a photon with a specific wavelength that corresponds to the energy difference, and it would typically be within the visible or UV range of the electromagnetic spectrum depending on the specific transition.