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QPages 416-417: Q1: HC Verma: Concepts of Physics - Volume 2 Semiconductors and Semiconductor Devices Pages 416-417: Q1 Solution: How many 1s energy states are present in one mole of sodium…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often count one state per orbital per atom, forgetting that each orbital has two spin‑degenerate states; thus a mole of atoms provides $2N_A$ states for any given $ns$ orbital. The 1s orbital is fully occupied (2 electrons/atom) while the 3s orbital has only one electron/atom, so only half of its $2N_A$ states are filled.

How many 1s energy states are present in one mole of sodium vapour? Are they all filled in normal conditions? How many 3s energy states are present in one mole of sodium vapour? Are they all filled in normal conditions?

Step-by-Step Verified Solution

**Answer:** The number of 1s energy states in one mole of sodium vapour is 2N_A, and they are all filled. The number of 3s energy states is 2N_A, and they are half-filled (only one electron per sodium atom occupies the 3s band). **Step-by-Step Explanation:** Sodium (Z = 11) has electronic configuration 1s_ 2s_ 2p_ 3s_. The 1s band can hold 2 electrons per atom. In one mole (N_A atoms), there are 2N_A states in the 1s band, all filled. The 3s band can also hold 2 electrons per atom, giving 2N_A states. Sodium has only one 3s electron per atom, so the 3s band is half-filled .

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