QuestionJune 26, 2025

Rank the following orbitals in order of increasing number of nodes. 1slt 2s=2plt 3s=3d 1slt 2slt 3slt 2plt 3d 1slt 2s=2plt 3slt 3d 1slt 2slt 3slt 2p=3d 1slt 2slt 2plt 3slt 3d

Rank the following orbitals in order of increasing number of nodes. 1slt 2s=2plt 3s=3d 1slt 2slt 3slt 2plt 3d 1slt 2s=2plt 3slt 3d 1slt 2slt 3slt 2p=3d 1slt 2slt 2plt 3slt 3d
Rank the following orbitals in order of increasing number of nodes.
1slt 2s=2plt 3s=3d
1slt 2slt 3slt 2plt 3d
1slt 2s=2plt 3slt 3d
1slt 2slt 3slt 2p=3d
1slt 2slt 2plt 3slt 3d

Solution
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Answer

1s\lt 2p=3d\lt 2s\lt 3s Explanation 1. Determine the number of nodes Nodes in an orbital are given by n - l - 1, where n is the principal quantum number and l is the azimuthal quantum number. - **1s**: n=1, l=0 \Rightarrow 1 - 0 - 1 = 0 nodes. - **2s**: n=2, l=0 \Rightarrow 2 - 0 - 1 = 1 node. - **2p**: n=2, l=1 \Rightarrow 2 - 1 - 1 = 0 nodes. - **3s**: n=3, l=0 \Rightarrow 3 - 0 - 1 = 2 nodes. - **3d**: n=3, l=2 \Rightarrow 3 - 2 - 1 = 0 nodes. 2. Rank orbitals by nodes Order them based on increasing number of nodes: 1s (0) < 2p (0) < 3d (0) < 2s (1) < 3s (2).

Explanation

1. Determine the number of nodes<br /> Nodes in an orbital are given by $n - l - 1$, where $n$ is the principal quantum number and $l$ is the azimuthal quantum number. <br /><br />- **1s**: $n=1, l=0 \Rightarrow 1 - 0 - 1 = 0$ nodes.<br />- **2s**: $n=2, l=0 \Rightarrow 2 - 0 - 1 = 1$ node.<br />- **2p**: $n=2, l=1 \Rightarrow 2 - 1 - 1 = 0$ nodes.<br />- **3s**: $n=3, l=0 \Rightarrow 3 - 0 - 1 = 2$ nodes.<br />- **3d**: $n=3, l=2 \Rightarrow 3 - 2 - 1 = 0$ nodes.<br /><br />2. Rank orbitals by nodes<br /> Order them based on increasing number of nodes: $1s (0) < 2p (0) < 3d (0) < 2s (1) < 3s (2)$.
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