Which is a correct set of values of [tex]$m$[/tex] for one of the subshells of [tex]$n=2$[/tex]?
A. [tex]$-1,0,1$[/tex]
B. [tex]$-1,-2,0,1,2$[/tex]
C. [tex]$-1,-2,-3,0,1,2,3$[/tex]
D. [tex]$-1,-2,-3,-4,0,1,2,3,4$[/tex]
Answer (2)
The correct set of values of the magnetic quantum number m for one of the subshells of n = 2 is option A: − 1 , 0 , 1 , which corresponds to the p subshell where l = 1 . The values − 1 , 0 , 1 represent all possible orientations of the p-orbitals. Other given options do not fit the criteria for m at the n = 2 energy level.
;
The possible values of the azimuthal quantum number l for n = 2 are 0 and 1 .
For l = 0 , the possible value of m is 0 .
For l = 1 , the possible values of m are − 1 , 0 , 1 .
Therefore, the correct set of values of m is − 1 , 0 , 1 .
Explanation
Understanding the Problem We are given the principal quantum number n = 2 and asked to find a correct set of values for the magnetic quantum number m for one of the subshells.
Finding Possible Values of l The possible values of the azimuthal quantum number l are 0 , 1 , ... , n − 1 . For n = 2 , the possible values of l are 0 and 1 .
Determining Possible Values of m For each value of l , the magnetic quantum number m can take values from − l to + l , i.e., − l , − l + 1 , ... , 0 , ... , l − 1 , l .
Case l=0 If l = 0 , the only possible value for m is 0 .
Case l=1 If l = 1 , the possible values for m are − 1 , 0 , 1 .
Checking the Options Now we check the given options to see which one matches the possible values of m for either l = 0 or l = 1 . The option − 1 , 0 , 1 matches the possible values of m for l = 1 .
Examples
Understanding quantum numbers helps in predicting the electronic configuration of atoms, which is crucial in chemistry for understanding chemical bonding and the properties of materials. For example, knowing the possible values of m for a given l allows us to determine the number of orbitals in a subshell, which directly relates to the number of electrons that can occupy that subshell. This knowledge is essential in fields like materials science and quantum computing.
