d orbital
The dxy orbital has two nodal planes perpendicular to the xy plane, passing through the nucleus. These nodal planes result in regions of zero probability of finding an electron in the dxy orbital.
A Px orbital has 1 nodal plane. This nodal plane passes through the nucleus and divides the orbital into two lobes along the x-axis.
The d orbital.An s orbital has one lobe and no nodal plane passing through the nucleus.A p orbitals has two lobes and one nodal plane.* A d orbital has four lobes and twonodal planes.An f orbital has eight lobes of maximum electron probability separated by three nodal planes.General Chemistry, Atoms First, 1st Addition, McMurry & Fay
The angular momentum quantum number, symbolized by l, indicates the shape of an orbital.
The angular momentum number shows the shape of the electron cloud or the orbital. The magnetic quantum number, on the other hand, determines the number of orbitals and their orientation within a subshell.
In molecular orbital theory, a node is a region in a molecular orbital where the probability of finding an electron is zero. A nodal plane is a two-dimensional surface through which no electron can pass, resulting in a node in the molecular orbital. Nodes play a crucial role in determining the shape and energy of molecular orbitals.
There are 3 nodes present in a 4f orbital: one radial node and two angular nodes. This means that there are regions in the orbital where the probability of finding an electron is zero.
In chemistry, pi bonds (π bonds) are covalent chemical bonds where two lobes of one involved electron orbital overlap two lobes of the other involved electron orbital. Only one of the orbital's nodal planes passes through both of the involved nuclei.
A sigma bond is a molecular bond made by the joining of the wavefunctions of either an s to an s orbital, an s to a pz orbital, a pz to a pz orbital or a dz2 to a dz2 orbital. Sigma bonds are the strongest of the molecular bonds (the others being the pi and delta bonds) and has the maximum electron density directly between the nuclei with no nodal planes and cylindrical symmetry (for the bonding variety, since sigma antibonds have no electron density between the nuclei). For bonds between small elements (such as hydrogen, carbon, oxygen), one bond in a single, double, or triple bond is always a sigma bond (the others are pi bonds).
In quantum mechanics, Clebsch-Gordan coefficients are used to determine the possible total angular momentum states when combining two angular momenta. For example, when combining the spin of an electron with the orbital angular momentum of an atom, Clebsch-Gordan coefficients help calculate the probabilities of different total angular momentum states that can result from this combination.
Each electron in an atom is in an orbital (*NOT* an orbit!!) at a specific energy level from the positive nucleus. The energy levels of these orbitals are fixed -- an electron can go from orbital 's' to orbital 'p', but it can't go halfway between these two orbitals. When an electron in an atom goes from a higher orbital to a lower one, then the atom must give off an amount of energy, that is exactly the difference in energy in the two levels. For a hydrogen atom, these orbital levels are fixed by the fact that the angular momentum of an electron in an orbital is quantized -- ie, it comes in exact multiples, but not fractions, of a minimal amount.
Each electron in an atom is in an orbital (*NOT* an orbit!!) at a specific energy level from the positive nucleus. The energy levels of these orbitals are fixed -- an electron can go from orbital 's' to orbital 'p', but it can't go halfway between these two orbitals. When an electron in an atom goes from a higher orbital to a lower one, then the atom must give off an amount of energy, that is exactly the difference in energy in the two levels. For a hydrogen atom, these orbital levels are fixed by the fact that the angular momentum of an electron in an orbital is quantized -- ie, it comes in exact multiples, but not fractions, of a minimal amount.