The four quantum numbers that describe the state of an electron 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 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, and the following six electrons occupy the 2p orbitals. The 11th electron will occupy the 3s orbital.
Principal quantum number (n): The 3s orbital corresponds to the principal quantum number of 3. Therefore, the value of n is 3.
Azimuthal quantum number (l): The azimuthal quantum number describes the shape of the orbital. In the case of the 3s orbital, l has a value of 0. The range of l values is from 0 to (n-1), so for the 3rd principal energy level (n=3), l can take values of 0, 1, and 2.
Magnetic quantum number (m_l): The magnetic quantum number describes the orientation of the orbital in space. For the 3s orbital (l=0), there is only one possible orientation, which means m_l has a value of 0.
Spin quantum number (m_s): The spin quantum number describes the spin state of the electron, which can be either +1/2 (spin-up) or -1/2 (spin-down). This quantum number does not depend on the electron's position or orbital. It is generally represented as either up arrow ↑ or down arrow ↓. The specific value of m_s for the 11th electron of sodium is not given in the electron configuration alone and would require further information.
Therefore, the three known quantum numbers for the 11th electron of sodium are: n = 3 l = 0 m_l = 0
Keep in mind that the specific spin quantum number (m_s) is not determined solely by the electron configuration and would require additional information to determine if it is spin-up (+1/2) or spin-down (-1/2).