To understand the problem, we need to evaluate the energy changes as an electron transitions between different energy levels in a hydrogen atom.
First, we evaluate the energy absorbed when the electron moves from level 1 (n=1) to level 4 (n=4). The energy levels of the electron in a hydrogen atom are given by the formula:
[tex]\[ E_n = -\frac{13.6 \text{ eV}}{n^2} \][/tex]
1. Energy at level 1 (n=1):
[tex]\[ E_1 = -\frac{13.6 \text{ eV}}{1^2} = -13.6 \text{ eV} \][/tex]
2. Energy at level 4 (n=4):
[tex]\[ E_4 = -\frac{13.6 \text{ eV}}{4^2} = -\frac{13.6 \text{ eV}}{16} = -0.85 \text{ eV} \][/tex]
Next, we determine the energy absorbed when moving from level 1 to level 4 by finding the energy difference between these two levels:
[tex]\[ \text{Energy absorbed} = E_4 - E_1 = -0.85 \text{ eV} - (-13.6 \text{ eV}) = 12.75 \text{ eV} \][/tex]
The electron then drops from level 4 to level 2. We need to calculate the energy at level 2 (n=2):
[tex]\[ E_2 = -\frac{13.6 \text{ eV}}{2^2} = -\frac{13.6 \text{ eV}}{4} = -3.4 \text{ eV} \][/tex]
We then determine the energy released when the electron moves from level 4 to level 2:
[tex]\[ \text{Energy released} = E_2 - E_4 = -3.4 \text{ eV} - (-0.85 \text{ eV}) = -3.4 \text{ eV} + 0.85 \text{ eV} = -2.55 \text{ eV} \][/tex]
By comparing the magnitudes of the absorbed and released energies, we find:
- Energy absorbed when moving from level 1 to level 4 is [tex]\( 12.75 \text{ eV} \)[/tex]
- Energy released when moving from level 4 to level 2 is [tex]\( -2.55 \text{ eV} \)[/tex] (the negative sign indicates a release of energy)
Thus, the energy absorbed in the first move is greater than the energy released in the second move.
Therefore, the correct statement is:
The energy absorbed in the first move is greater than the energy released in the second move.
