Which of the following statement(s) is/are true?

$$\textbf{A.}$$ If two orbitals have the same value of $$(n + l)$$, the orbital with lower value of $$n$$ will have lower energy.

$$\textbf{B.}$$ Energies of the orbitals in the same subshell increase with increase in atomic number.

$$\textbf{C.}$$ The size of $$2p_x$$ orbital is less than the size of $$3p_x$$ orbital.

$$\textbf{D.}$$ 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:

Statement A

According to the $$(n+l)$$ rule:

• Orbital with lower $$(n+l)$$ value has lower energy.
• If $$(n+l)$$ values are equal, orbital with lower $$n$$ has lower energy.

Example:

• $$3p:n+l=3+1=4$$
• $$4s:n+l=4+0=4$$

Since $$3p$$ has lower n, it has lower energy.

Statement A is true.

Statement B

For orbitals belonging to the same subshell (same $$n$$ and $$l$$), energy does not simply increase with atomic number. Only in hydrogen-like atoms, orbitals of same shell are degenerate (have same energy level), and in multi-electron atoms the trend is not stated this way.

Statement B is false.

Statement C

Size of orbitals generally increases with principal quantum number $$n$$.

Thus:

$$size(2p_x)<size(3p_x)$$

Statement C is true.

Statement D

Number of radial nodes:

Radial nodes=$$n−l−1$$

Calculate:

• $$5f:5−3−1=1$$
• $$6s:6−0−1=5$$
• $$4d:4−2−1=1$$
• $$5p:5−1−1=3$$
• $$5d:5−2−1=2$$

So $$5d$$ has 2 radial nodes.

Therefore the statement “none have 2 radial nodes” is false.

Statement D is False