Question

In an atom, how many electrons can have
(i) n = 4 (ii) m1 =1 (iii) ms = ½

Answer 1

Correct Answer: 3

To solve how many electrons can have specific quantum numbers, let's break it down for each part:

(i) n = 4: The principal quantum number \( n \) determines the energy level and can hold a maximum of \( 2n^2 \) electrons. For \( n = 4 \):
Max electrons = \( 2(4)^2 = 32 \).

(ii) m_l = 1: The magnetic quantum number \( m_l \) ranges from \(-l\) to \(+l\), where \( l \) is the azimuthal quantum number corresponding to each sublevel (s, p, d, f, etc.). Different values of \( l \) allow \( m_l = 1 \):

• For \( l = 1 \) (p sublevel), \( m_l = -1, 0, 1 \) → 2 electrons can have \( m_l = 1 \). 
• For \( l = 2 \) (d sublevel), \( m_l = -2, -1, 0, 1, 2 \) → 2 electrons per magnetic quantum state.
• For \( l = 3 \) (f sublevel), possibilities increase similarly but note the electron pairing per value.

(iii) m_s = ½: The spin quantum number \( m_s \) has two possible values: \( +\frac{1}{2} \) or \(-\frac{1}{2}\). In any orbital, one electron can have \( m_{s\) = ½.}

Conclusion: While evaluating all possibilities and given the involved energy levels, each condition typically supports a distribution such that the numbers will align closely within expected catagories of energy level, sublevels, and degeneracy of orbital state in complex atoms. For precise configurations, distinct configurations can emerge in computation based on other quantum mechanical considerations.