which orbitals have centre of symmetry
The orbitals that have a center of symmetry are called "symmetric orbitals" or "s-orbitals". These orbitals have a spherical shape and are denoted by the letter "s".
To determine if an orbital has a center of symmetry, you can examine its mathematical equation. The s-orbitals in the atomic orbitals of hydrogen, for example, have the following equations:
1s orbital: Ψ = (1/√π)(1/a₀)^(3/2)e^(-r/a₀)
2s orbital: Ψ = (1/√4π)(1/a₀)^(3/2)(2-r/a₀)e^(-r/2a₀)
3s orbital: Ψ = (1/√81π)(1/a₀)^(3/2)(3-2r/a₀+(2/9)(r/a₀)^2)e^(-r/3a₀)
In these equations, "a₀" represents the Bohr radius and "r" represents the distance from the nucleus.
By examining these equations, you can see that the s-orbitals have a radial component that depends only on the distance from the nucleus (r), leading to a spherical symmetry. This means that s-orbitals have a center of symmetry at the nucleus.
In contrast, other types of orbitals such as p, d, and f orbitals do not possess a center of symmetry. These orbitals have a more complex shape due to their angular components, which results in multiple lobes or nodal planes without a center of symmetry.