To find the energy of the electron in the $n = 5$ level for a hydrogen atom, we can use the energy level formula for hydrogen atoms:

$E_n = \frac{-2.18 \times 10^{-18} \, \text{J}}{n^2}$

Where:

• $E_n$ is the energy of the electron in the $n$-th energy level,
• $n$ is the principal quantum number (in this case $n = 5$),
• $-2.18 \times 10^{-18} \, \text{J}$ is the energy of the electron in the $n = 1$ level.

Now, we can plug $n = 5$ into the formula:

$E_5 = \frac{-2.18 \times 10^{-18} \, \text{J}}{5^2} = \frac{-2.18 \times 10^{-18} \, \text{J}}{25}$

Let's calculate the energy for $n = 5$.The energy of the electron in the $n = 5$ energy level of a hydrogen atom is approximately $-8.72 \times 10^{-20} \, \text{J}$.

Do you have any questions or need further clarification?

Here are five related questions to consider:

1. How does the energy of an electron change as the value of $n$ increases?
2. What is the significance of negative energy values for electron levels in hydrogen atoms?
3. How would the energy change if we considered an atom with more than one electron?
4. Can you calculate the wavelength of light required to excite an electron from $n = 5$ to $n = 1$?
5. How do energy levels differ between hydrogen and heavier atoms?

Tip: As $n$ increases, the energy levels get closer together, which means that the energy difference between consecutive levels decreases.