The solutions to the Schrdinger equation for the electron in a hydrogen atom have three quantum numbers

The solutions to the Schrödinger equation for the electron in a hydrogen atom have three quantum numbers associated with them, called n, l, and m, and these solutions are denoted by ψ_nlm.

(a)?The ψ_210?function is given by

where a₀ = 0.529 × 10^??10 m is called the Bohr radius. Write this function in terms of Cartesian coordinates.

(b)?The ψ₂₁₁ function is given by

Write an expression for the magnitude of this complex function.

(c) The ψ₂₁₁ function is sometimes called ψ_2p1. Write expressions for the real and imaginary parts of the function, which are proportional to the related functions. which are called ψ_2px and ψ_2py.