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Chapter 6: Problem 63

Sketch the shape and orientation of the following types of orbitals: \((\mathbf{a}) s,(\mathbf{b}) p_{z},(\mathbf{c}) d_{x y}\).

Short Answer

Expert verified
The s orbital is spherical with no specific orientation. The p_z orbital has a dumbbell shape along the z-axis, with two lobes connected by a nodal plane. The d_xy orbital has four lobes in the xy plane, forming an "X" shape when viewed from above.

Step by step solution

01

Sketch the s orbital

The s orbital is the simplest of all types of orbitals. It is spherical in shape, with the nucleus of the atom at the center. The s orbital doesn't have any specific orientation since it is symmetrical in all three dimensions. When sketching, draw a small circle to represent the nucleus, and then a larger circle around it that represents the s orbital. The space inside the large circle is where the electron is most likely to be found.
02

Sketch the p_z orbital

The p_z orbital is one of the three p orbitals. It has a dumbbell shape along the z-axis. To sketch the p_z orbital, draw the nucleus, and then two lobes (oval shapes) above and below the nucleus, representing the regions with a high probability of finding the electron. The lobes should be connected by a thin line that represents the nodal plane, which is an area with minimal likelihood of finding the electron. Label the vertical axis as 'z', showing that the orbital lies along this axis.
03

Sketch the d_xy orbital

The d_xy orbital is a d orbital and has a more complex shape. It consists of four lobes located in the xy plane, with each lobe pointing towards the corners of the x and y axes. To sketch the d_xy orbital, draw the nucleus and then add four lobes in the xy plane with two lobes on either side of the nucleus. These lobes should form an "X" shape when viewed from above. Label the axes as 'x' and 'y' to show that the orbital lies in the xy plane.

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