The four quantum numbers that describe an electron in an atom are the principal quantum number (n), the azimuthal quantum number (l), the magnetic quantum number (m_l), and the spin quantum number (m_s).
To determine the quantum numbers for the 11th electron of sodium (Na), we first need to understand the electron configuration of sodium.
The electron configuration of sodium is 1s² 2s² 2p⁶ 3s¹. This means that the first two electrons occupy the 1s orbital, the next two electrons occupy the 2s orbital, the following six electrons occupy the 2p orbitals, and the 11th electron occupies the 3s orbital.
Principal quantum number (n): The 3s orbital corresponds to the principal quantum number n = 3.
Azimuthal quantum number (l): The azimuthal quantum number represents the subshell within a principal energy level. For the 3s orbital, the azimuthal quantum number l = 0.
Magnetic quantum number (m_l): The magnetic quantum number determines the orientation of the orbital within a subshell. For the 3s orbital, the magnetic quantum number can have only one value, which is m_l = 0.
Spin quantum number (m_s): The spin quantum number describes the spin orientation of an electron. It can have two values: +1/2 or -1/2. The 11th electron in sodium will have a spin quantum number of m_s = +1/2 or -1/2.
In summary, the four quantum numbers for the 11th electron of sodium (Na) are:
n = 3 (principal quantum number) l = 0 (azimuthal quantum number) m_l = 0 (magnetic quantum number) m_s = +1/2 or -1/2 (spin quantum number)