Question

If \(n\) and \(l\) represent the principal and azimuthal quantum numbers respectively, the formula used to know the number of radial nodes possible for a given orbital is:

• A. \(n - l\)
• B. \(n - l + 1\)
• C. \(n - l - 1\)
• D. \(n - 2\) \vspace{0.5cm}

Hint:

The number of radial nodes is important in quantum mechanics as it relates to the regions in an atom where the probability of finding an electron is zero. The formula \(n - l - 1\) helps to quickly calculate this.

Answer 1

The Correct Option is C

Step 1: Formula for Radial Nodes The number of radial nodes in an orbital is determined by the formula: \[ \text{Number of radial nodes} = n - l - 1 \] Where: - \(n\) is the principal quantum number, - \(l\) is the azimuthal quantum number. Step 2: Explanation of Radial Nodes Radial nodes are regions where the probability density function of an electron becomes zero due to changes in the radial distance from the nucleus. The number of radial nodes depends on the values of \(n\) and \(l\). As the value of \(n\) increases, more radial nodes are created, while the number of nodes is reduced as \(l\) increases. Step 3: Applying the Formula For a given orbital: - If \(n = 3\) and \(l = 1\), then the number of radial nodes is: \[ n - l - 1 = 3 - 1 - 1 = 1 \] Thus, the number of radial nodes is 1 for this orbital. \vspace{0.5cm}