How does the energy of a principal energy level depend on the value of n? Does a higher value of n mean a higher or lower energy?

E= 2.180E-19 J x (1/n^2)

The energy of a principal energy level in an atom depends on the value of the principal quantum number, denoted as "n". The principal quantum number determines the size and energy of the orbital.

The energy of a principal energy level increases as the value of "n" increases. In other words, a higher value of "n" corresponds to a higher energy level. This means that electrons in higher energy levels are farther from the nucleus and have more energy.

To determine the energy of a specific energy level, you can use the equation:

E = -13.6 eV/n^2

Where "E" is the energy of the level in electron volts (eV) and "n" is the principal quantum number.

For example, if you have an electron in the second energy level (n = 2), you can plug it into the equation:

E = -13.6 eV/2^2
E = -13.6 eV/4
E = -3.4 eV

So, the energy of the second energy level would be -3.4 electron volts.

Remember, this equation gives the energy relative to the nucleus, so it represents the energy of an electron in an atom.