Which of the following is a possible set of n, l, mi, and ms quantum numbers for the last electron added to form a gallium atom (Z=31)?
4,1,1,1/2
You're question isn't clear and you listed only one choice; however, what you have listed is the possible choice for the 4p1 electron added.
To determine if the given set of quantum numbers is possible for the last electron added to form a gallium atom (Z=31), we need to consider the principles governing the assignment of quantum numbers.
The quantum numbers describe various properties and characteristics of an electron within an atom. The four quantum numbers are:
1. Principal Quantum Number (n): It determines the energy level or shell of the electron.
2. Angular Momentum Quantum Number (l): It indicates the shape of the electron's orbital.
3. Magnetic Quantum Number (mᵢ): It specifies the orientation of the orbital within a given subshell.
4. Spin Quantum Number (mₛ): It represents the spin of the electron.
For an atom with atomic number (Z), the maximum value of n is equal to Z. In the case of gallium (Z=31), the maximum value of n is 31.
Looking at the given set of quantum numbers: 4, 1, 1, 1/2
1. Principal Quantum Number (n): The value of n is 4. Since 4 is less than 31 (atomic number of gallium), it is a possible value.
2. Angular Momentum Quantum Number (l): The value of l is 1. The valid range for l is from 0 to n-1. In this case, since n is 4, the range for l is 0 to 3. Therefore, l = 1 is a possible value.
3. Magnetic Quantum Number (mᵢ): The value of mᵢ is 1. The range for mᵢ is from -l to +l. In this case, since l is 1, the range for mᵢ is -1 to +1. Therefore, mᵢ = 1 is a possible value.
4. Spin Quantum Number (mₛ): The value of mₛ is 1/2. Spin quantum number can have two possible values, +1/2 or -1/2, representing the two possible spin orientations of an electron. So, mₛ = 1/2 is a possible value.
Therefore, the given set of quantum numbers: (n, l, mᵢ, mₛ) = (4, 1, 1, 1/2) is a possible set for the last electron added to form a gallium atom (Z=31).