Saved Febury 21, 2005735AM 2. It an electron were to fall down to the E_(1) level from the E_(3) level, how would its energy compare to one that only fell to the E_(2) level? Explain. Symbols Record Answer Sentence Starters

## Step 1: <br />The energy levels in an atom are quantized, meaning that electrons can only occupy certain discrete energy levels. The energy of an electron in an atom is determined by the principal quantum number, which is denoted by the energy level number.<br /><br />## Step 2:<br />In this case, the electron is falling from the $E_{3}$ level to the $E_{1}$ level. This means it is losing energy as it moves to a lower energy level.<br /><br />## Step 3:<br />Similarly, if the electron were to fall from the $E_{3}$ level to the $E_{2}$ level, it would also lose energy as it moves to a lower energy level.<br /><br />## Step 4:<br />However, the amount of energy lost would be greater when the electron falls from the $E_{3}$ level to the $E_{1}$ level compared to when it falls from the $E_{3}$ level to the $E_{2}$ level. This is because the energy difference between the $E_{1}$ and $E_{3}$ levels is greater than the energy difference between the $E_{2}$ and $E_{3}$ levels.<br /><br />### The formula for the energy difference between two levels is given by: <br />### \( \Delta E = E_{final} - E_{initial} \)<br /><br />## Step 5:<br />Therefore, the electron that falls from the $E_{3}$ level to the $E_{1}$ level would have a lower energy compared to the electron that only falls to the $E_{2}$ level.