Question: 50: Identify the incorrect statement from the following.
(1) In an atom, all the five 3 d orbitals are equal in energy in free state.
(2) The shapes of d_{x y}, d_{y z} and d_{z x} orbitals are similar to each other; and d_{x^{2}-y^{2}} and d_{z^{2}} are similar to each other.
(3) All the five 5 d orbitals are different in size when compared to the respective 4 d orbitals.
(4) All the five 4 d orbitals have shapes similar to the respective 3 d orbitals.
Answer: Option (2)
Explanation:
In a free atom, all the orbitals belonging to the same subshell have the same energy.
Therefore, all the five 3 d orbitals are degenerate in energy,
making statement (1) correct.
Orbitals of higher principal quantum number have larger size.
Hence, all the five 5 d orbitals are larger in size compared to the corresponding
4 d orbitals, so statement (3) is correct.
The shape of an orbital depends on the azimuthal quantum number and the type of orbital,
not on the principal quantum number.
Thus, 4 d orbitals have shapes similar to the corresponding 3 d orbitals, making statement (4) correct.
Among the five d orbitals, d_{x y}, d_{y z} and d_{z x} have similar shapes and form one group.
However, d_{x^{2}-y^{2}} and d_{z^{2}} do not have similar shapes.
The d_{z^{2}} orbital has a unique shape with a doughnut-shaped ring,
unlike d_{x^{2}-y^{2}}.
Therefore, statement (2) is incorrect.