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Which of the following orbitals are vali...

Which of the following orbitals are valid?
`1s, 2p_(x),3d_(x^(2)-z^(2)),4p_(z),2p_(y),3d_(x^(2)),2d_(x^(2)-y^(2)),4d_(z^(2))`

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To determine which of the given orbitals are valid, we need to consider the rules governing the quantum numbers associated with atomic orbitals. The principal quantum number (n), azimuthal quantum number (l), and magnetic quantum number (m_l) must all adhere to specific constraints. ### Step-by-Step Solution: 1. **Identify the Validity of Each Orbital**: - **1s**: - Principal quantum number (n) = 1 - Azimuthal quantum number (l) = 0 (s orbital) - Valid: Yes, because l = 0 is allowed for n = 1. - **2p_x**: - n = 2, l = 1 (p orbital) - Valid: Yes, because l = 1 is allowed for n = 2. - **3d_(x²-z²)**: - n = 3, l = 2 (d orbital) - Valid: Yes, because l = 2 is allowed for n = 3. - **4p_z**: - n = 4, l = 1 (p orbital) - Valid: Yes, because l = 1 is allowed for n = 4. - **2p_y**: - n = 2, l = 1 (p orbital) - Valid: Yes, because l = 1 is allowed for n = 2. - **3d_(x²)**: - n = 3, l = 2 (d orbital) - Valid: Yes, because l = 2 is allowed for n = 3. - **2d_(x²-y²)**: - n = 2, l = 2 (d orbital) - Valid: No, because l = 2 is not allowed for n = 2 (it can only be 0 or 1). - **4d_(z²)**: - n = 4, l = 2 (d orbital) - Valid: Yes, because l = 2 is allowed for n = 4. 2. **List of Valid Orbitals**: - Valid: 1s, 2p_x, 3d_(x²-z²), 4p_z, 2p_y, 3d_(x²), 4d_(z²) - Invalid: 2d_(x²-y²) ### Final Answer: The valid orbitals from the given list are: **1s, 2p_x, 3d_(x²-z²), 4p_z, 2p_y, 3d_(x²), 4d_(z²)**. The invalid orbital is **2d_(x²-y²)**.
To determine which of the given orbitals are valid, we need to consider the rules governing the quantum numbers associated with atomic orbitals. The principal quantum number (n), azimuthal quantum number (l), and magnetic quantum number (m_l) must all adhere to specific constraints. ### Step-by-Step Solution: 1. **Identify the Validity of Each Orbital**: - **1s**: - Principal quantum number (n) = 1 - Azimuthal quantum number (l) = 0 (s orbital) ...
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