Concepts Of Physics MCQ Edition [Volume 2]PhysicsSemiconductors and Semiconductor Devices
Determine the number of states per cubic metre in the 3s band of sodium, given that its density is 1013 kg m ⁻³ . Additionally, find how many of these states are empty.
Options
- A1.06 10²⁹ and 5.3 10²⁸
- B5.3 10²⁸ and 2.65 10²⁸
- C2.65 10²⁸ and 1.33 10²⁸
- D5.3 10²⁸ and 5.3 10²⁸
Correct answer
B. 5.3 10²⁸ and 2.65 10²⁸
Step-by-step solution
The number of sodium atoms per cubic metre is given by: n = N_A M Substituting the given values, = 1013 kg m ⁻³ , N_A = 6.022 10²³ mol ⁻¹ , and M = 23 10⁻³ kg mol ⁻¹ : n = 1013 6.022 10²³ 23 10⁻³ 2.65 10²⁸ m ⁻³ Each sodium atom contributes one 3s orbital to the 3s band. Since each orbital can accommodate 2 electrons (spin up and spin down), the total number of states per cubic metre in the 3s band is: N_ states = 2n = 2 2.65 10²⁸ = 5.3 10²⁸ Sodium has one valence electron per atom in the 3s state. Thus, the number