An electron in a hydrogen atom is excited from the ground state to the n=5 state

Question

An electron in a hydrogen atom is excited from the ground state to the n=5 state. Decide whether the following statements are true or false?

A. n=5 is the first excited state

B. It take more energy to ionize (remove) the electron from n=5 then from the ground state

C. The electron that is farther from the nucleus (on average) is n=5 than in the ground state

D. The wavelength of light emitted when the electron drops from n=5 to n=1 is longer than that from n=5 to n=2

E. The wavelength the atom absorbs in going from n=1 to n=5 is the same that emmited as it goes from n=5 to n=1

Explanation / Answer

A) FALSE. For n=5 the electron is in an excited state. But it is not the first excited state.

B) FALSE. It takes less energy to ionize the electron from n=5 state than from the ground state.
If the electron is further from the nucleus, it will take less energy to get to the n = infinity state, in which the electron leaves the influence of its nucleus.

C) TRUE. The electron is closer to the nucleus on average in the n=1 state than in the n=5 state.
As the number of electron shells increases, the electron is farther from the nucleus on average.

D) FALSE. The wavelength of light emitted if the electron drops from n=5 to n=2 will be shorter than the wavelength of light emitted when the electron falls from n=5 to n=1. A larger drop in energy states results in a larger energy change. The change from n=5 to n=1 is a larger difference in energy states, and will result in more energy released when the electron falls to the lower state. This corresponds to a larger frequency of the photons emitted, and a smaller wavelength for the n=5 to n=1 transition.

E) TRUE. The wavelength of light emitted when the electron falls to the ground state from n=5 will be the same as the wavelength of light absorbed to go from the ground state to n=5. The difference in the energy states is fixed, so it does not matter whether the electron gains energy to go to the excited state or whether the electron emits energy in the form of a photon when it falls back. The same difference is present, which means that the wavelength of energy will be identical.

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