Final answer:
The maximum number of electrons in an atom for given quantum numbers n and l are calculated using the general formula 2(2l + 1). For the given cases, (a) n=3 and l=2 yields 10 electrons, (b) n=4 and l=3 yields 14 electrons, (c) n=2 and l=1 yields 6 electrons, and (d) n=5 and l=4 yields 18 electrons.
Step-by-step explanation:
The student is asking about the maximum number of electrons that can reside in the atomic orbitals within a principal quantum shell (n) and an azimuthal quantum number (l). The general formula to determine the maximum number of electrons within a subshell is 2(2l + 1).
To calculate the maximum number of electrons in various orbitals with given values of n and l, we can apply this formula for each case provided: (a) For n = 3 and l = 2 (which represents the 3d orbital), the maximum number of electrons is 2(2*2 + 1) = 2(5) = 10. (b) For n = 4 and l = 3 (which represents the 4f orbital), the maximum number of electrons is 2(2*3 + 1) = 2(7) = 14.
(c) For n = 2 and l = 1 (which represents the 2p orbital), the maximum number of electrons is 2(2*1 + 1) = 2(3) = 6. (d) For n = 5 and l = 4 (which represents the 5g orbital), the maximum number of electrons is 2(2*4 + 1) = 2(9) = 18. The maximum number of electrons that can be in a shell overall is given by the formula 2n². Therefore, the student can use these formulas to correctly identify the maximum number of electrons for each combination of n and l given.