Final answer:
Silicon has 4 electrons with the quantum number n=3, occupying the 3s and 3p orbitals in its ground-state electron configuration.
Step-by-step explanation:
The student has asked how many electrons in silicon have the quantum number n=3. Silicon (Si) has an atomic number of 14, which means it has 14 electrons. The electron configuration of silicon is 1s²2s²2p¶3s²3p². It can be seen from this configuration that there are a total of 10 electrons in the n=1 and n=2 shells (1s²2s²2p¶). Thus, in the n=3 shell, only the 3s and 3p orbitals are occupied.
The 3s orbital has 2 electrons and the 3p orbital has 2 electrons, making it a total of 4 electrons that have the principal quantum number n=3 for silicon. It is essential to understand the way orbitals are filled, where electrons occupy the lowest energy orbitals first (Aufbau principle), and each orbital can contain a maximum of 2 electrons with opposite spins, as per the Pauli exclusion principle.