Question

Match the LIST-I with LIST-II

Choose the correct answer from the options given below:

• A. A-IV, B-I, C-III, D-II
• B. A-IV, B-II, C-III, D-I
• C. A-III, B-I, C-IV, D-II
• D. A-IV, B-III, C-II, D-I

Hint:

Remember that Radial nodes = n - l - 1 and Nodal planes = l. Calculate these values for each given orbital and match them with the statements in List-II.

Answer 1

The Correct Option is D

Concept: In quantum mechanics, nodes are regions where the probability density of finding an electron is zero. Total nodes = $n - 1$. These are divided into radial nodes and angular nodes (nodal planes).

Step 1: Identify $n$ and $l$ for each orbital.
- 2s: $n=2, l=0$
- 3s: $n=3, l=0$
- 3p: $n=3, l=1$
- 4d: $n=4, l=2$

Step 2: Apply the node formulas.
Radial Nodes ($R$) = $n - l - 1$
Angular Nodes ($A$) = $l$

Step 3: Calculate values for each match.
A (2s): $R = 2-0-1 = 1$, $A = 0$. Result: 1 Radial node, 0 Nodal plane. Match: IV.
B (3s): $R = 3-0-1 = 2$, $A = 0$. Result: 2 Radial nodes, 0 Nodal plane. Match: III.
C (3p): $R = 3-1-1 = 1$, $A = 1$. Result: 1 Radial node, 1 Nodal plane. Match: II.
D (4d): $R = 4-2-1 = 1$, $A = 2$. Result: 1 Radial node, 2 Nodal planes. Match: I.

Step 4: Final Sequence Check.
A $\rightarrow$ IV
B $\rightarrow$ III
C $\rightarrow$ II
D $\rightarrow$ I
The correct combination is A-IV, B-III, C-II, D-I.