Final answer:
A photon beam of energy 12.1 eV can excite the electron of a hydrogen atom from the ground state to the 3rd orbit, given that the energy difference between these levels matches the photon's energy. Bohr's model and the formula for energy levels of a hydrogen atom have been applied to solve for the correct orbit. Option B is the correct answer.
Step-by-step explanation:
To find out to which orbit the electron of a hydrogen atom may be excited by a photon beam of energy 12.1 eV, we must consider the energy levels of a hydrogen atom as described by Bohr's theory. The energy levels of the hydrogen atom are given by the formula E_n = -13.6 eV/n2, where E_n is the energy of the n-th level and n is the principal quantum number.
The ground state of a hydrogen atom, or the first energy level, has an energy of -13.6 eV. To move an electron from the ground state to a higher orbit (excited state), a photon must have energy equal to the difference between the higher energy state E_n and the ground state energy.
For example, to move the electron to the 2nd level (n = 2), the energy needed is E_2 - E_1 = (-13.6 eV/22) - (-13.6 eV) = -3.4 eV - (-13.6 eV) = 10.2 eV
To move the electron to the 3rd level (n = 3), the energy needed is E_3 - E_1 = (-13.6 eV/32) - (-13.6 eV) = -1.51 eV - (-13.6 eV) = 12.09 eV
Thus, a photon beam with energy of 12.1 eV can excite an electron from the ground state to the 3rd level, since 12.1 eV is sufficient to bridge the energy gap between the 1st and 3rd levels.
The correct answer is (b) 3rd orbit.