Final answer:
The quantum numbers for the 3s orbital are n=3, l=0, m₁=0; for the 4p orbital, n=4, l=1, with m₁ ranging from -1 to +1; and for the 3d orbital, n=3, l=2, with m₁ ranging from -2 to +2. For all orbitals mₛ can be either +1/2 or -1/2 representing electron spin.
Step-by-step explanation:
The values of the four quantum numbers of an electron in the mentioned orbitals, namely 3s, 4p, and 3d, can be understood by examining each quantum number in turn. The primary quantum number (n) indicates the energy level and approximate radial distance from the nucleus. The angular momentum quantum number (l) defines the shape of the orbital. The magnetic quantum number (m₁) specifies the orbital's orientation in space. Lastly, the spin quantum number (mₛ) indicates the spin direction of the electron.
- For the 3s orbital: n = 3, l = 0 (since s orbitals have l = 0), m₁ = 0 (only one orientation for s orbitals), mₛ can be either +1/2 or -1/2.
- For the 4p orbital: n = 4, l = 1 (p orbitals have l = 1), m₁ can be -1, 0, or +1 (three orientations for p orbitals), mₛ can be either +1/2 or -1/2.
- For the 3d orbital: n = 3, l = 2 (d orbitals have l = 2), m₁ can be -2, -1, 0, +1, or +2 (five orientations for d orbitals), mₛ can be either +1/2 or -1/2.