To determine the correct possible values of [tex]\( l \)[/tex] for [tex]\( n = 4 \)[/tex], we analyze the constraints and properties typically observed in mathematical and physical contexts, particularly in quantum mechanics where [tex]\( l \)[/tex] often represents the azimuthal or orbital angular momentum quantum number. The allowed values of [tex]\( l \)[/tex] are non-negative integers that range from [tex]\( 0 \)[/tex] to [tex]\( n-1 \)[/tex].
Given [tex]\( n = 4 \)[/tex]:
1. The lowest possible value of [tex]\( l \)[/tex] is [tex]\( 0 \)[/tex].
2. The highest possible value of [tex]\( l \)[/tex] is [tex]\( n-1 \)[/tex], which is [tex]\( 4-1 = 3 \)[/tex].
Therefore, the possible values of [tex]\( l \)[/tex] are all the integers from [tex]\( 0 \)[/tex] to [tex]\( 3 \)[/tex]. So, the correct list of possible values for [tex]\( l \)[/tex] is [tex]\( 0, 1, 2, 3 \)[/tex].
Among the given options, the correct set of possible values for [tex]\( l \)[/tex] is:
[tex]\[
0, 1, 2, 3
\][/tex]
Hence, the first option is the correct answer.
