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In order for the atom to be shown in its ground state, the number of arrows/the direction they are facing/how they are spaced must all be correct. For part a, the number of arrows (6 - the atomic number of Carbon) is correct, but the two arrows in 2p should be in two separate boxes and should be facing the same way (up). It is easier for them to go into separate orbitals, even though the first box is not filled yet. Going into separate boxes/orbitals also accounts for why they should have a parallel spin (both arrows facing the same direction). Thus, part a is not in its ground state because the arrows are spaced differently and are facing opposite directions. For part b, the arrow in the middle box for 2p is facing in the opposite direction, which should not happen since the electrons are in separate orbitals and should all be facing the same direction (parallel spin). For part c, there is an arrow in the box for 2p, but the orbital for 2s has not yet been filled with two electrons. The atom cannot move up to 2p unless it has filled the 2s orbitals or the atom has been excited (increased in energy). Thus, the atom is in an excited rather than a ground state. Part d is the only option which shows the right number, direction, and spacing of arrows in the electron configuration.
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