3. What is the difference measured in energy when an electron falls from E_(3) to E_(1) ? How many times greater is this value as compared to the difference of the electron falling from E_(3) to E_(2)

To determine the difference in energy when an electron falls from $E_{3}$ to $E_{1}$, we need to calculate the absolute value of the difference between these two energy levels.<br /><br />The energy difference between $E_{3}$ and $E_{1}$ is given by:<br /><br />$E_{3} - E_{1} = -1.51 \, \text{eV} - (-3.40 \, \text{eV}) = 1.89 \, \text{eV}$<br /><br />Therefore, the energy difference when an electron falls from $E_{3}$ to $E_{1}$ is 1.89 eV.<br /><br />To determine how many times greater this value is compared to the difference of the electron falling from $E_{3}$ to $E_{2}$, we need to calculate the absolute value of the difference between these two energy levels.<br /><br />The energy difference between $E_{3}$ and $E_{2}$ is given by:<br /><br />$E_{3} - E_{2} = -1.51 \, \text{eV} - (-3.00 \, \text{eV}) = 1.49 \, \text{eV}$<br /><br />Therefore, the energy difference when an electron falls from $E_{3}$ to $E_{2}$ is 1.49 eV.<br /><br />To find out how many times greater the energy difference from $E_{3}$ to $E_{1}$ is compared to the energy difference from $E_{3}$ to $E_{2}$, we can divide the two values:<br /><br />$\frac{1.89 \, \text{eV}}{1.49 \, \text{eV}} \approx 1.27$<br /><br />Therefore, the energy difference when an electron falls from $E_{3}$ to $E_{1}$ is approximately 1.27 times greater than the energy difference when an electron falls from $E_{3}$ to $E_{2}$.