Question: Part A: Which of the following gives the correct permitted values of ml for l=2?
Part B: A second important result is that electrons will fill the lowest energy states available. This would seem to indicate that every electron in an atom should be in the n=1 state. This is not the case, because of Pauli's exclusion principle. The exclusion principle says that no two electrons can occupy the same state. A state is completely characterized by the four numbers n, l, ml, and ms, where ms is the spin of the electron.
An important question is, How many states are possible for a given set of quantum numbers? For instance, n=1 means that l=0 with ml=0 are the only possible values for those variables. Thus, there are two possible states: (1, 0, 0, 1/2) and (1, 0, 0, ?1/2). How many states are possible for n=2? Express your answer as an integer.
Part C: Because the amount of screening of the nucleus is related to distance from the nucleus, the sand p subshells of a many-electron atom with the same value of n are not of equal energy, as they are in hydrogen. An electron in the p subshell has a lower probability of being inside the electrons of the n=1 shell than does an electron in the s subshell. Thus, the nucleus is screened somewhat more completely for electrons in the p subshell than for electrons in the ssubshell. This makes states in the p subshell of higher energy than states in the s subshell.
The electron structure of an atom shows how many electrons are in each subshell. For instance, helium's electron structure is written 1s2, signifying the two electrons in the 1ssubshell. Neon, with ten electrons, has electron structure 1s22s22p6, signifying two electrons in the 1s subshell, two in the 2s subshell, and six in the 2p subshell. Observe that the exponents sum to the number of electrons in the atom.
Which of the following is not a valid electron structure for an atom in its ground state? Use the fact that electrons fill the lowest energy states first and keep in mind the number of allowed states for each subshell.