The distance of an atomic orbital from the nucleus is primarily determined by two factors: the principal quantum number (n) and the shape of the orbital.
Principal Quantum Number (n): The principal quantum number determines the energy level or shell of the electron. It can have positive integer values starting from 1 (n = 1), representing the closest shell to the nucleus. As the value of n increases, the electron is found in successively higher energy levels, farther away from the nucleus. Therefore, orbitals with higher principal quantum numbers are generally found at greater distances from the nucleus.
Shape of the Orbital: Each principal energy level (n) contains one or more subshells, which correspond to different shapes of orbitals. The shape of the orbital affects its average distance from the nucleus. The most commonly encountered orbitals are s, p, d, and f orbitals.
s Orbitals: Spherical in shape, s orbitals have no angular nodes and are centered on the nucleus. As the principal quantum number increases, the size of the s orbital increases, and it occupies more space farther from the nucleus.
p Orbitals: P orbitals have a dumbbell shape with two lobes separated by a nodal plane. Each p orbital (px, py, and pz) lies along one of the three Cartesian axes. The distance of a p orbital from the nucleus depends on the value of the principal quantum number (n) but is generally greater than that of an s orbital with the same value of n.
d and f Orbitals: These orbitals have more complex shapes and contain multiple nodal planes. They have higher energy than s and p orbitals and are found farther away from the nucleus.
It's important to note that these factors provide a general understanding of orbital distance trends. However, the actual electron distribution around an atom is described by quantum mechanics and can be influenced by additional factors such as electron-electron repulsion and the presence of other atoms or molecules in the vicinity.