Final answer:
The highest excited state that hydrogen atoms can reach with 12.2 eV is the state where n=4. This is because the ionization energy from the n=4 state is 0.85 eV according to the energy levels of hydrogen, and 12.2 eV is more than enough to excite an electron to the n=4 level.
Step-by-step explanation:
The highest excited state that unexcited horizontal hydrogen atoms can reach when they are bombarded with 12.2 eV electrons is determined by the energy levels of hydrogen. In hydrogen, the energy levels are quantized and can be described by the Rydberg formula or using the Bohr model where the energy for a particular orbit (or state) is given by -13.6 eV/n². Given that 12.2 eV is the energy being provided, we can determine which energy level (n) the electron will reach without exceeding this energy.
Since the ground state (n=1) has an energy of -13.6 eV, the first excited state (n=2) would have an energy of -13.6 eV/2² = -13.6 eV/4 = -3.4 eV. The electron in the hydrogen atom can occupy this state when it gains 3.4 eV from its ground state. To ionize an electron from the n=2 state, the energy required would be the energy to remove it from this state and bring it to zero energy level, which would be a total of 3.4 eV.
Going up further, the second excited state (n=3) has an energy of -13.6 eV/3² = -13.6 eV/9= -1.51 eV, and the energy required to ionize from the n=3 state would be 1.51 eV. Therefore, continuing with this process and finding the highest n before the energy exceeds 12.2 eV will lead us to the answer.
For the third excited state (n=4), the energy is -13.6 eV/4² = -13.6 eV/16 = -0.85 eV and the ionization energy from this state is precisely 0.85 eV as ionization removes an electron, bringing its state to zero energy. Therefore, since 12.2 eV is higher than the energy necessary to ionize from the n=4 state by a significant amount, we can say that with 12.2 eV, we can reach at least the n=4 level.
Hence, by applying the energy considerations for each state, we can conclude that the correct answer would be:
d) n=4