Calculate the energy needed to ionize an electron of H atoms from its second excited state.
E = 2.180E-18(1/2^2 - 1/0)
the right answer is 2.42x10^-19J. but once i plug the numbers on my calculator i get an error message.
You got an error message because 1/0 is an indeterminate. I didn't know how to write 1/infinity but that's what it should have been and 1/infinity is 0. As to the other, I guess I don't know what the second excited state is. I assumed it was with the electron in n = 2; I guess that is right so I don't know what second excited state means.
To calculate the energy needed to ionize an electron from the second excited state of a hydrogen atom, we need to determine the energy difference between the initial and final states.
The energy of an electron in a hydrogen atom can be calculated using the Rydberg formula:
E = -13.6 eV / n²
where E is the energy of the electron, n is the principal quantum number of the energy level.
In this case, the second excited state corresponds to n = 3. So, we can calculate the energy of the initial state:
E_initial = -13.6 eV / (3²) = -13.6 eV / 9 = -1.511 eV
To calculate the energy needed to ionize the electron, we need to consider that the final state corresponds to an ionized atom, where the electron is completely removed. In this case, the energy of the final state is zero, since there is no binding energy anymore.
Therefore, the energy needed to ionize the electron from the second excited state is:
Energy needed = E_final - E_initial = 0 - (-1.511 eV) = 1.511 eV
Therefore, the energy needed to ionize an electron from the second excited state of a hydrogen atom is 1.511 eV.