Electronic Structure of Atoms Practice Questions & Answers

The principal quantum number $(n)$(n) indicates the main energy level or shell. As $n​$n​ increases, the energy of the electron increases and it is, on average, found further from the nucleus.

The angular momentum quantum number $l​$l​ can take integer values from $0​$0​ to $n-1$n−1. For $n=3$n=3, the possible values for $l​$l​ are $0, 1,$0,1, and $2​$2​.

For any given shell $n​$n​, the maximum value of $l​$l​ is $n-1$n−1. In option $(b)$(b), $n=2$n=2, so the maximum allowed $l​$l​ is $1​$1​. Therefore, $l=2$l=2 is impossible.

The letter designations for subshells are based on the value of $l​$l​: $l=0 \rightarrow s$l=0→s, $l=1 \rightarrow p$l=1→p, $l=2 \rightarrow d$l=2→d, $l=3 \rightarrow f$l=3→f.

The maximum number of electrons in a shell is given by the formula $2n^2$2n2. For $n=3$n=3, $2(3)^2 = 2(9) = 18$2(3)2=2(9)=18 electrons.

A $d​$d​ subshell corresponds to $l=2$l=2. The number of orbitals is given by $2l + 1$2l+1. For $l=2$l=2, $2(2)+1 = 5$2(2)+1=5 orbitals (with $m_l$ml​ values $-2, -1, 0, +1, +2$−2,−1,0,+1,+2).

An $s​$s​ orbital ($l=0$l=0) is spherically symmetrical around the nucleus.

The magnetic quantum number $(m_l)$(ml​) describes the orientation of the orbital in space relative to the other orbitals.

The Aufbau Principle (German for 'building up') states that electrons occupy the lowest energy orbitals first.

The Pauli Exclusion Principle states that no two electrons can have the same four quantum numbers; therefore, an orbital can hold a maximum of two electrons with opposite spins.