Question

What is the physical significance of the value of ${\mathit{\psi }}^{\mathbf{2}}$at a particular point in an atomic orbital?

Short answer

${\psi }^2$is a probability factor and describes the probability of finding an electron within a small space.

Step-by-step solution

Discuss about the Schrodinger’s equation:

$\frac{d^2\psi }{d{x}^2}+\frac{d^2\psi }{d{y}^2}+\frac{d^2\psi }{d{z}^2}+\frac{8\mathrm{\pi m}}{h^2}(E-V)\psi =0$

Where

$x,y,z\to$Cartesian coordinates of electron

$m\to$mass of electron

$E\to$the total energy of the election

$V\to$the potential energy of the electron

$h\to$Planck's constant

$\psi \to$the wave function of electron

Now explain the signification of ψ2 :

${\psi }^2$is known as probability density and it determines the probability of finding an electron within a small space.

If${\psi }^2=0$ , the probability of finding an electron is negligible at that point.

If ${\psi }^2$the value is large, the electron is present at that place for a longer duration.

If ${\psi }^2$the value is small, the probability of finding an electron is low at that point.