An energetically excited hydrogen atom has its electron in a 5f subshell. The electron drops down to the 3d subshell, releasing a photon in the process. (c) The hydrogen atom now has a single electron in the 3d subshell. What is the energy in kJ/mol required to remove this electron?

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Identify the principal quantum number (n) for the 3d subshell, which is n=3.

Use the formula for the energy of an electron in a hydrogen atom, E = -2.18 \(\times\) 10^{-18} J \(\times\) \(\left\)(\(\frac{1}{n^2}\)\(\right\)), substituting n=3 to find the energy of the electron in the 3d subshell.

Convert the energy from joules to kilojoules by dividing by 1000.

Since the question asks for the energy per mole, convert the energy from kJ to kJ/mol by multiplying by Avogadro's number, 6.022 \(\times\) 10^{23} mol^{-1}.

The result from the previous step gives the ionization energy required to remove the electron from the 3d subshell of a hydrogen atom in kJ/mol.

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주요 개념

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Electron Configuration

Electron configuration describes the distribution of electrons in an atom's orbitals. For hydrogen, which has only one electron, the configuration is typically 1s¹. When the electron transitions between energy levels, such as from 5f to 3d, it changes its energy state, which is crucial for understanding the energy required to remove the electron.

Ionization Energy

Ionization energy is the energy required to remove an electron from an atom in its gaseous state. For hydrogen, this energy varies depending on the electron's energy level. When the electron is in the 3d subshell, the ionization energy will be different from that of the ground state, reflecting the stability and energy of the electron's current state.

Photon Emission

Photon emission occurs when an electron transitions from a higher energy level to a lower one, releasing energy in the form of a photon. This process is fundamental in understanding how energy levels in atoms work, as the energy of the emitted photon corresponds to the difference in energy between the two levels. This concept is essential for calculating the energy required to remove the electron after it has transitioned.