Given, (A) n = 5, m_l = −1 (B) n = 3, l = 2, m_l = −1, m_s = +1/2 The maximum number of electron(s) in an atom that can have the quantum numbers as given in (A) and (B) respectively are :

The maximum number of electrons in an atom that can have given quantum numbers

Q. Given,

(A) $ n = 5,\; m_l = -1 $

(B) $ n = 3,\; l = 2,\; m_l = -1,\; m_s = +\frac{1}{2} $

The maximum number of electron(s) in an atom that can have the quantum numbers as given in (A) and (B) respectively are :

A. 4 and 1

B. 2 and 4

C. 26 and 1

D. 8 and 1

Correct Answer: 8 and 1

Explanation

Case (A): $ n = 5 $ and $ m_l = -1 $ are given.

For a given principal quantum number $ n = 5 $, the possible values of azimuthal quantum number are:

$$ l = 0, 1, 2, 3, 4 $$

For a fixed value $ m_l = -1 $, only those values of $ l $ are allowed for which:

$$ -l \le m_l \le +l $$

So, $ m_l = -1 $ is possible for:

$$ l = 1, 2, 3, 4 $$

Thus, there are 4 different orbitals corresponding to $ m_l = -1 $.

Each orbital can accommodate 2 electrons due to two possible spin states:

$$ m_s = +\frac{1}{2},\; -\frac{1}{2} $$

Hence, maximum number of electrons for case (A) is:

$$ 4 \times 2 = 8 $$

Case (B): All four quantum numbers $ n = 3,\; l = 2,\; m_l = -1,\; m_s = +\frac{1}{2} $ are specified.

A unique set of four quantum numbers corresponds to only one electron.

Therefore, maximum number of electrons for case (B) is:

$$ 1 $$

Hence, the correct answer is:

$$ \boxed{8 \text{ and } 1} $$

Explanation

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