Question

solution of the schrodinger wave equation for the hydrogen atom results in a set of functions (orbitals) that describe the behavior of the electron.
erwin
schrodinger
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 (square) to (square)
the total number of orbitals possible at the ( n = 2 ) energy level is (square)
if the value of ( l = 0 )
the quantum number ( m ) can have values from (square) to (square)
the total number of orbitals possible at the ( l = 0 ) sublevel is (square)

Explanation:

Step1: Determine the range of \( l \) when \( n = 2 \)

The angular - momentum quantum number \( l \) has values from \( 0 \) to \( n - 1 \). When \( n=2 \), \( l = 0,1 \).

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

The formula for the total number of orbitals in a given energy level \( n \) is \( n^{2} \). When \( n = 2 \), the total number of orbitals is \( 2^{2}=4 \).

Step3: Determine the range of \( m \) when \( l = 0 \)

The magnetic quantum number \( m \) has values from \( -l \) to \( l \). When \( l = 0 \), \( m=0 \).

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

The number of orbitals for a given \( l \) is \( 2l + 1 \). When \( l = 0 \), the number of orbitals is \( 2\times0 + 1=1 \).

Answer:

• When \( n = 2 \), \( l \) ranges from \( 0 \) to \( 1 \), total number of orbitals at \( n = 2 \) is \( 4 \).
• When \( l = 0 \), \( m \) ranges from \( 0 \) to \( 0 \), total number of orbitals at \( l = 0 \) is \( 1 \).