Question

The electron density in the \[xy-plane\] in \[3{{d}_{{{x}^{2}}-{{y}^{2}}}}\] orbital is zero. If true enter 1, else enter 0.

Answer 1

Hint: In quantum chemistry electron density also known by electronic density generally measures the probability of an electron being present at an infinitesimal element of space surrounding any given point. It is a scalar quantity.

Complete Step by step solution: An orbital is the quantum mechanical advancement of Bohr’s orbit. In contrast to his concept of a simple circular orbit with a fixed radius, orbitals are defined as mathematically derived regions of space with different probabilities of containing an electron. The l value i.e. azimuthal quantum number is 2 which shows it has five d orbitals. The first principal shell to have a d subshell corresponds to n = 3. The five d orbitals show \[{{m}_{l}}\] values of −2, −1, 0, +1, and +2. The shape of 3d orbitals have more complex shapes than the 2p orbitals. All five 3d orbitals contain two nodal surfaces as compared to one for each p orbital and zero for each s orbital. In three of the d orbitals, the lobes of electron density are oriented between the x and y, x and z, and y and z planes and these orbitals are referred to as \[3{{d}_{xy}},3{{d}_{yz}},3{{d}_{zx}}\], fourth d orbital has lobes lying along the x and y axes shown as \[3{{d}_{{{x}^{2}}-{{y}^{2}}}}\] orbital and the fifth 3d orbital represented by \[3{{d}_{{{z}^{2}}}}\] and have a unique shape it looks like a orbital combined with an additional doughnut of electron probability lying in the xy plane. Electron density in the \[xy-plane\] in \[3{{d}_{{{x}^{2}}-{{y}^{2}}}}\] orbital is zero. As the lobes in the pz plane will be along the z axis and therefore the probability of finding electrons in the xy plane will be zero.

Hence we can say that the above statement is true and we can write it as 1.

Note: The energy of all five orbitals are equal but the first four orbitals are similar in shape to each other while the \[{{d}_{{{z}^{2}}}}\] differ from others. The radical node is zero. The \[{{d}_{xy}}\] orbital has two nodal planes passing through the origin and bisects the xy plane consisting of the z-axis. There are two angular nodes for d-orbital.