Question:
Consider the following statements.
(A) If two orbitals are having the same value of \(n+l\), then the orbital having the lower value of \(n\) will have lower energy.
(B) If atomic number increases, then the energy of orbitals belonging to a particular shell increases.
(C) Among 4s, 5d, 6f and 5p orbitals, none of these orbitals have two radial nodes.
(D) Size of 2\(p_x\) orbital is less than 3\(p_x\) orbital.
Which of the following statements are correct?
Consider the following statements.
(A) If two orbitals are having the same value of \(n+l\), then the orbital having the lower value of \(n\) will have lower energy.
(B) If atomic number increases, then the energy of orbitals belonging to a particular shell increases.
(C) Among 4s, 5d, 6f and 5p orbitals, none of these orbitals have two radial nodes.
(D) Size of 2\(p_x\) orbital is less than 3\(p_x\) orbital.
Which of the following statements are correct?
(A) If two orbitals are having the same value of \(n+l\), then the orbital having the lower value of \(n\) will have lower energy.
(B) If atomic number increases, then the energy of orbitals belonging to a particular shell increases.
(C) Among 4s, 5d, 6f and 5p orbitals, none of these orbitals have two radial nodes.
(D) Size of 2\(p_x\) orbital is less than 3\(p_x\) orbital.
Which of the following statements are correct?
Show Hint
When comparing orbitals with the same \(n+l\), remember that the lower \(n\) value corresponds to the lower energy. The size of orbitals increases with \(n\), so \(2p\) is smaller than \(3p\).
Updated On: Apr 7, 2026
- A and B are correct
- B and D are correct
- A and D are correct
- B and C are correct
Show Solution
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The Correct Option is C
Solution and Explanation
Step 1: Analyze Statement A.
The value of \(n+l\) determines the energy of orbitals. Orbitals with the same \(n+l\) value are degenerate, and within this group, orbitals with a lower \(n\) value have lower energy. This is consistent with the fact that as the principal quantum number \(n\) increases, the orbital is further from the nucleus and thus has higher energy.
Therefore, Statement A is correct.
Step 2: Analyze Statement B.
If the atomic number increases, the nuclear charge increases, causing a stronger attraction between the nucleus and electrons. This pulls the electrons closer, decreasing the energy of orbitals, not increasing it. Therefore, Statement B is incorrect.
Step 3: Analyze Statement C.
The number of radial nodes in an orbital is given by the formula:
\[ \text{Radial nodes} = n - l - 1 \] For 4s: \(n = 4, l = 0\), so the number of radial nodes is \(4 - 0 - 1 = 3\).
For 5d: \(n = 5, l = 2\), so the number of radial nodes is \(5 - 2 - 1 = 2\).
For 6f: \(n = 6, l = 3\), so the number of radial nodes is \(6 - 3 - 1 = 2\).
For 5p: \(n = 5, l = 1\), so the number of radial nodes is \(5 - 1 - 1 = 3\).
Since these orbitals have radial nodes, Statement C is incorrect.
Step 4: Analyze Statement D.
The size of orbitals increases with the principal quantum number \(n\). Since the \(2p_x\) orbital has a smaller \(n\) than the \(3p_x\) orbital, the size of the 2p orbital is indeed smaller than the size of the 3p orbital. Therefore, Statement D is correct.
Step 5: Conclusion.
Statements A and D are correct, while Statements B and C are incorrect.
Final Answer: (C) A and D are correct
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