Which of the following statement(s) is/are true ? A. If two...

Statement A: According to the $(n+l)$ rule, if two orbitals have the same $(n+l)$ value, the orbital with the lower value of $n$ has lower energy. This statement is true.

Statement B: As the atomic number increases, the effective nuclear charge ($Z_{eff}$) increases. The energy of an orbital is proportional to $-\dfrac{Z_{eff}^2}{n^2}$. Thus, the energy becomes more negative, meaning the energy of the orbitals in the same subshell decreases with an increase in atomic number. This statement is false.

Statement C: The size of an orbital increases with an increase in the principal quantum number $n$. Therefore, the size of the $2p_x$ orbital is less than the size of the $3p_x$ orbital. This statement is true.

Statement D: The number of radial nodes is given by the formula $n - l - 1$.
For $5f$: $5 - 3 - 1 = 1$
For $6s$: $6 - 0 - 1 = 5$
For $4d$: $4 - 2 - 1 = 1$
For $5p$: $5 - 1 - 1 = 3$
For $5d$: $5 - 2 - 1 = 2$
Since the $5d$ orbital has exactly $2$ radial nodes, the statement that none of the orbitals have $2$ radial nodes is false.

Therefore, only statements A and C are true.

Answer: A and C only