Question

The maximum number of electrons in the following two given set of quantum numbers (i) \( n = 5, \, m_l = -1 \) and (ii) \( n = 4, \, \ell = 2, \, m_l = 1, \, m_s = \frac{1}{2} \) respectively is:

• A. 8, 1
• B. 4, 1
• C. 26, 2
• D. 10, 2

Hint:

When determining the maximum number of electrons, remember that the number of orbitals in a subshell is determined by the value of \( \ell \), and each orbital can hold two electrons with opposite spins.

Answer 1

The Correct Option is A

Step 1: Understanding the quantum numbers.
For \( n = 5, \, \ell = 1, \, m_l = -1 \), the possible orbitals are the p orbitals. Since each p orbital can hold 2 electrons, and there are 4 orbitals (because \( m_l = -1 \) allows for 4 orientations), this gives us a total of 8 electrons.
Step 2: Applying quantum numbers for the second case.
For \( n = 4, \, \ell = 2, \, m_l = 1, \, m_s = \frac{1}{2} \), there are 5 possible orbitals (the d subshell). Each orbital can hold only 1 electron due to the given value of \( m_s \), so this gives us a total of 1 electron.
Step 3: Conclusion.
Thus, the correct answer is (1), 8 electrons and 1 electron, respectively.