Sure, here's a brief summary of the different types of orbitals and their shapes and orientations:

s orbital: The s orbital is spherical in shape and has no nodal planes. It is centered around the nucleus and is symmetrical in all directions.

p orbital: The p orbital is dumbbell-shaped and has two lobes pointing in opposite directions along each of the three Cartesian axes. There are three different p orbitals: px, py, and pz, each oriented along one of the x, y, or z-axes respectively.

d orbital: The d orbital is more complex in shape and has four lobes pointing in different directions, with two nodal planes that pass through the nucleus. There are five different d orbitals: dxy, dyz, dxz, dx2-y2, and dz2, each oriented in a different direction in space.

f orbital: The f orbital is even more complex in shape, with multiple lobes and nodal planes. There are seven different f orbitals, each oriented in a different direction in space.

The shape and orientation of each orbital is determined by the values of the three quantum numbers (n, l, and m) that define it. The principal quantum number (n) determines the energy level of the electron, the angular momentum quantum number (l) determines the shape of the orbital, and the magnetic quantum number (m) determines the orientation of the orbital in space.
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