Final answer:
The greatest frequency photon in a hydrogen atom is emitted during the transition from n = 2 to n = 1, which is not explicitly listed but implied as the highest energy transition available from the provided options.
Step-by-step explanation:
n = 2 to n = 1, The transition in a hydrogen atom that would emit the photon of the greatest frequency is the transition from a higher energy level to the lowest energy level, which is from an excited state to the ground state (n = 1). In the given choices, however, the largest energy transition would be from n = 2 to n = 1, which is not listed. Since we are limited to the options provided, we look for the transition with the highest initial n value, which in this case is from n = 2 to n = 1, answer option A. This transition is not the Balmer series but rather the Lyman series in the hydrogen emission spectrum, which is known to have higher frequencies as it involves dropping to the first energy level.
According to the Bohr model of the atom, the frequency of the emitted photon is proportional to the energy difference between the initial and the final states. Since the energy levels are quantized and the energy difference increases significantly as the electron moves closer to the ground state, the transition from n = 2 to n = 1 will yield the highest frequency photon among the listed transitions.The transition in a hydrogen atom that would emit the photon of the greatest frequency is option D: n = 4 to n = 5.The frequency of a photon is directly proportional to the difference in energy between the two energy levels involved in the transition. The higher the energy difference, the higher the frequency of the emitted photon. In this case, the transition from n = 4 to n = 5 has the highest energy difference, resulting in the greatest frequencyFor example, the n = 4 to n = 5 transition corresponds to the emission of a photon with a frequency of about 7.49 x 10^14 Hz (hertz), while the other transitions have lower frequencies.