Question

wave functions describe orbitals in a hydrogen atom. each function is characterized by 3 quantum numbers: n, l, and m. if the value of n = 2: the quantum number l can have values from to . the total number of orbitals possible at the n = 2 energy level is . if the value of l = 0: the quantum number m can have values from to . the total number of orbitals possible at the l = 0 sublevel is .

Explanation:

Step1: Determine the values of \( l \) for \( n = 2 \)

The quantum number \( l \) can have values from \( 0 \) to \( n - 1 \). For \( n = 2 \), \( l = 0,1 \).

Step2: Calculate the total number of orbitals for \( n = 2 \)

The formula for the total number of orbitals in a shell with principal quantum number \( n \) is \( n^{2} \). For \( n = 2 \), \( 2^{2}=4 \).

Step3: Determine the values of \( m \) for \( l = 0 \)

The magnetic quantum number \( m \) can have values from \( -l \) to \( +l \). For \( l = 0 \), \( m = 0 \).

Step4: Calculate the total number of orbitals for \( l = 0 \)

The number of orbitals for a given \( l \) is \( 2l + 1 \). For \( l = 0 \), \( 2(0)+1 = 1 \).

Answer:

The quantum number \( l \) can have values from \( 0 \) to \( 1 \). The total number of orbitals at the \( n = 2 \) energy level is \( 4 \). If the value of \( l = 0 \), the quantum number \( m \) can have values from \( 0 \) to \( 0 \). The total number of orbitals possible at the \( l = 0 \) sublevel is \( 1 \).