How many possible values of the magnetic quantum number, m_l, are allowed for an electron in a 5f subshell?

• A. 9
• B. 3
• C. 7
• D. 5

Answer: (C)

Verified step by step guidance

1. Identify the azimuthal quantum number \( l \) for the given subshell. For an \( f \) subshell, \( l = 3 \).
2. Recall that the magnetic quantum number \( m_l \) can take integer values from \( -l \) to \( +l \), including zero.
3. Write down the possible values of \( m_l \) for \( l = 3 \): \( -3, -2, -1, 0, +1, +2, +3 \).
4. Count the total number of possible \( m_l \) values. Since it ranges from \( -l \) to \( +l \), the total number is \( 2l + 1 \).
5. Calculate \( 2l + 1 = 2 \times 3 + 1 \) to find the number of allowed \( m_l \) values for the 5f subshell.