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p Orbitals
These are the axes.
Yes., and their being along the coordinate axes does not change the answer.Consider the vectors: i, -i and j where i is the unit vector along the x axis and j along the y axis. The resultant of the three is j.
Vector A is parallel to the cross product of vectors B and C, and it is parallel to the axis that neither B or C lie along if the two other axes are defined as the axes that B and C lie along.
x2/a2 + y2/b2 = 1, is the equation of an ellipse with semi-major axes a and b (that's the equivalent of the radius, along the two different axes), centered in the origin.
p Orbitals
A p orbital is the type of orbital with five positions on the axes: one along each of the x, y, and z axes, and two alternating along each pair of axes. The shape of a p orbital is typically dumbbell-shaped with lobes extending along the axes.
Subscripts such as y and xz in atomic orbitals indicate the orientation of the orbital in space. They correspond to the orientation of the lobes or regions of high electron density around the nucleus along different axes in three-dimensional space. The specific subscripts provide information about the spatial distribution and symmetry of the orbital.
There are a total of three p orbitals for an atom with principal quantum number n = 2: px, py, and pz. These orbitals are oriented along the x, y, and z axes.
P orbitals are dumbbell-shaped and have two lobes oriented along the perpendicular axes x, y, or z. The lobes have opposite phases resulting in a nodal plane within the orbital.
P orbitals at the same energy level have the same energy but differ in their spatial orientation. There are three p orbitals at each energy level (labeled as px, py, pz) that are oriented along the x, y, and z-axes, respectively. These orbitals have the same energy, but they have different spatial shapes and orientations.
There always three p orbitals in each energy level. They always have the same general shape, dumbbells pointing along the x, y, z axes. The difference is the "size" - 3p extend further than 2p
Hybridisation is a mathematical technique in valence bond theory used "create" new (higher energy) orbitals from base atomic orbitals so that the new orbitals point along bond axes. Valence bond theory as its name suggests focuses on the localised electron pair. Other bonding theories such as molecular orbital theory do not hybridise the base atomic orbitals. Both theories have their merits.
A tangent of the vector is the projection of a vector along the axes of a coordinate system.
Both the dxy and dx2-y2 orbitals belong to the d subshell and have four lobes. The main difference between them lies in their orientation in space. The dxy orbital lies in between the x and y axes, while the dx2-y2 orbital lies along the x and y axes.
The shape of the p subshell is predicted to be dumbbell or peanut-shaped. It is composed of three p orbitals, each oriented along one of the three coordinate axes (x, y, z). These orbitals have two lobes of electron density with a node at the center.
The shape of the 3p atomic orbital is a dumbbell shape, with two lobes oriented along the x, y, or z axes. Each lobe has the same probability of finding the electron.