Question

Minimum number of nodes are present in

• A. 2s
• B. 3s
• C. 4s
• D. 5s

Hint:

To find the number of nodes in an orbital, use the formula \( \text{Number of nodes} = n - l - 1 \). The lower the \(n\) value, the fewer the nodes.

Answer 1

The Correct Option is A

In quantum mechanics, the number of nodes in an atomic orbital is given by the formula: \[ \text{Number of nodes} = n - l - 1 \] where: - \(n\) is the principal quantum number, - \(l\) is the azimuthal quantum number. For each orbital: 1. 2s orbital has \(n = 2\) and \(l = 0\), so the number of nodes is: \[ 2 - 0 - 1 = 1 \text{ node} \] 2. 3s orbital has \(n = 3\) and \(l = 0\), so the number of nodes is: \[ 3 - 0 - 1 = 2 \text{ nodes} \] 3. 4s orbital has \(n = 4\) and \(l = 0\), so the number of nodes is: \[ 4 - 0 - 1 = 3 \text{ nodes} \] 4. 5s orbital has \(n = 5\) and \(l = 0\), so the number of nodes is: \[ 5 - 0 - 1 = 4 \text{ nodes} \] Thus, the minimum number of nodes is in the 2s orbital.