How much energy is required to ionize hydrogen when it is in the state with

n = 6? (answer in eV)

To calculate the energy required to ionize hydrogen, we need to determine the difference in energy between the initial state (n=6) and the final state (n=infinity, or when the electron is completely removed from the atom).

The energy of a hydrogen atom in a particular energy level is given by the Rydberg formula:

E = -13.6 eV / n^2

Where E is the energy, n is the principal quantum number, and -13.6 eV is the ionization energy of hydrogen.

So for the initial state with n=6, we can calculate the energy:

E_initial = -13.6 eV / 6^2
= -13.6 eV / 36
= -0.3778 eV

Now, to find the energy required to ionize hydrogen, we subtract the energy of the final state (n=infinity) from the initial state:

E_required = E_initial - E_final

Since E_final is when n=infinity, the energy of the final state is zero.

E_required = -0.3778 eV - 0 eV
= -0.3778 eV

Therefore, the energy required to ionize hydrogen when it is in the state with n=6 is approximately -0.3778 eV.