Question

what is the maximum number of electrons that can have n=4, m_l=3 in an atom?

Explanation:

Step1: Recall quantum number rules

The principal quantum number \( n = 4 \), magnetic quantum number \( m_l=3 \). For a given \( m_l \), the spin quantum number \( m_s \) can have two values: \( +\frac{1}{2} \) and \( -\frac{1}{2} \).

Step2: Determine electron count

Each orbital (defined by a unique set of \( n, l, m_l \)) can hold a maximum of 2 electrons (due to two possible spin states). Since \( m_l = 3 \) defines a specific orbital (for a given \( n \) and \( l \) where \( l\geq3 \), here \( n = 4 \), possible \( l \) values are 0,1,2,3; when \( l = 3 \), \( m_l \) ranges from - 3 to 3, so \( m_l = 3 \) is valid), the number of electrons with \( n = 4 \) and \( m_l = 3 \) is determined by the spin states. So the number of electrons is 2 (one with \( m_s=+\frac{1}{2} \) and one with \( m_s = -\frac{1}{2} \)).

Answer:

2