To determine the maximum number of electrons with principal quantum number n = 3 and spin quantum number m_s = -1/2, we need to understand the quantum numbers and how they define electron orbitals.

Step 1: Understand Quantum Numbers
For a given principal quantum number n, the number of orbitals is given by n². Each orbital can hold a maximum of 2 electrons, one with m_s = +1/2 and the other with m_s = -1/2.

Step 2: Calculate Total Orbitals for n=3
For n=3, total orbitals = n² = 9.

Step 3: Determine Electrons with m_s = -1/2
Since each orbital has one electron with m_s = -1/2, the number of such electrons is equal to the number of orbitals. Therefore, for n=3, it is 9.

Final Answer: The maximum number of electrons with n=3 and m_s = -1/2 is 9.

Related Topics

Quantum Numbers: Quantum numbers describe the properties of atomic orbitals and the electrons in them. The principal quantum number (n) defines the energy level, the azimuthal quantum number (l) defines the subshell, the magnetic quantum number (m_l) defines the orbital, and the spin quantum number (m_s) defines the electron spin.

Formulae

Total number of orbitals for a given n: $n^2$

Total number of electrons for a given n: $2n^2$