Question

Which principal energy level change by the electron of a hydrogen atom will cause the greatest amount of energy to be absorbed?

1. n = 2 to n = 4
2. n = 2 to n = 5
3. n = 4 to n = 2
4. n = 5 to n = 2

Answer 1

The transition in a hydrogen atom that causes the greatest amount of energy to be absorbed is n = 2 to n = 5, as it represents the largest increase in the principal quantum number, indicating a move to a higher, more energetic state.

Step-by-step explanation:

In the context of hydrogen atoms, when an electron transitions between energy levels, the greatest amount of energy is absorbed during the transition covers the largest difference in the principal quantum number n. According to the Bohr model, the energy levels of a hydrogen atom are quantized and can be expressed by the formula En = -13.6 eV / n2, where n is the principal quantum number and the energy for n = 1 is the ground state energy of hydrogen.

To determine which transition absorbs the most energy, we compare the transitions given. The energy absorbed or emitted during a transition is given by the difference in energy between the final and initial states, ΔE = Efinal - Einitial. In the case of absorption, ΔE will be positive and larger if the final state is much higher than the initial state.

For absorption, we only consider options 1 and 2. Transitioning from n = 2 to n = 5 will have a greater energy change compared to transitioning from n = 2 to n = 4, because the quantum level change is larger, going to a higher energy level. Therefore, the answer is the second option, n = 2 to n = 5.

Answer 2

The transition from n = 2 to n = 5 will cause the greatest amount of energy to be absorbed by the electron of a hydrogen atom, because it corresponds to the largest increase in the principal quantum number, resulting in the largest energy difference.

Step-by-step explanation:

The principal energy level change by the electron of a hydrogen atom that will cause the greatest amount of energy to be absorbed corresponds to the transition that involves the greatest change in the principal quantum number, n. In Bohr's model of the hydrogen atom, the energy levels are quantized and their energy values are given by the formula En = -13.6 eV / n², where n is the principal quantum number. Thus, the greater the change in n, the larger the energy difference between the initial and final states.

Among the provided options:

• n = 2 to n = 4
• n = 2 to n = 5
• n = 4 to n = 2 (emission process)
• n = 5 to n = 2 (emission process)

The option with the highest n involved in the transition is from n = 2 to n = 5. This option will result in the largest absolute energy value being absorbed because it is the transition with the largest increase in the principal quantum number.