Question

Which of the following statement(s) is/are true?
A. If two orbitals have the same value of $(n+l)$, the orbital with lower value of $n$ will have lower energy.
B. Energies of the orbitals in the same subshell increase with increase in atomic number.
C. The size of $2p_x$ orbital is less than the size of $3p_x$ orbital.
D. Among 5f, 6s, 4d, 5p and 5d orbitals, none of the orbitals have 2 radial nodes.
Choose the correct answer from the options given below :

• A. A, B and C only
• B. A and C only
• C. C and D only
• D. A only

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This question tests fundamental principles of atomic structure, specifically the $(n+l)$ rule for orbital energy, orbital sizes, and the calculation of radial nodes.
Step 2: Detailed Explanation:
Statement A: This is the Aufbau principle's $(n+l)$ rule. If two orbitals have the same $(n+l)$ value, the one with the lower principal quantum number ($n$) is lower in energy (e.g., 3d has $n+l=5$ and 4p has $n+l=5$, but 3d is filled first). This is True.

Statement B: As the atomic number ($Z$) increases, the effective nuclear charge increases. This causes the orbital to be attracted more strongly toward the nucleus, which actually decreases the energy (makes it more negative). Thus, the statement is False.

Statement C: Orbital size is primarily determined by the principal quantum number $n$. Higher $n$ means the electron is likely further from the nucleus. Since $n=3$ for $3p_x$ and $n=2$ for $2p_x$, $3p_x$ is larger. This is True.

Statement D: Radial nodes are calculated as $n - l - 1$.
5f: $5 - 3 - 1 = 1$.
6s: $6 - 0 - 1 = 5$.
4d: $4 - 2 - 1 = 1$.
5p: $5 - 1 - 1 = 3$.
5d: $5 - 2 - 1 = 2$.
Since the 5d orbital does have 2 radial nodes, the statement "none of the orbitals have 2 radial nodes" is False.
Step 3: Final Answer:
Statements A and C are correct. Therefore, the answer is Option (B).