Answer:
1. - principal quantum number (n)
- orbital angular momentum quantum number (ℓ)
- magnetic quantum number (mℓ)
- electron spin quantum number (ms)
2. ℓ = 0, 1, 2, 3, 4, 5
3. mℓ = -5, -4, -3, -2, -1, 0 , 1, 2, 3, 4, 5
4. n = 9
Explanation:
1. Quantum numbers are values that describe the state of a physical system like an atom, nucleus or subatomic particles. In order to describe an electron in an atom, there are four quantum numbers needed. These are the principal quantum number or energy (n), the orbital angular momentum quantum number (ℓ), the magnetic quantum number (mℓ) and the electron spin quantum number (ms).
The principal quantum number (n) describes the ground state of an electron. It represents the energy level that an electron exists at. This uses whole numbers starting at n = 1 and continue until n = ∞.
The orbital angular momentum quantum number (ℓ) describes the shape of the orbital. It tells us the number of sublevels or subshells present in the main shell. Its value is equal to 0 until n-1.
The magnetic quantum number (mℓ) describes the orbital’s orientation in space. It informs the level of degeneracy of the orbitals. Its value is equal to – ℓ until + ℓ.
The electron spin quantum number (ms) describes the spin or direction in which the electron spins. This could either be an upward spin [tex](+\frac{1}{2})[/tex] or a downward spin [tex](-\frac{1}{2})[/tex].
2. For n = 6,
ℓ = 0 → n-1
ℓ = 0, 1, 2, 3, 4, 5
3. For n = 7 and ℓ = 5,
mℓ = - ℓ → + ℓ
mℓ = -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5
4. For ℓ = 0, 1, 2, 3, 4, 5, 6, 7, 8
n = 9 since there are 9 values of ℓ.
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