Quantum Mechanical Model of Atom and Concept of Atomic Orbitals

Calculation of no.of waves in an orbit :
\tt no.of \ waves = \frac{Circumference}{wavelength}
=\frac{3.33 \times \left(\frac{n^{2}}{Z}\right)Å}{3.33\left(\frac{n}{z}\right)Å}
n = orbit number

Total no.of revolutions per second :
\tt = \frac{velocity}{circumference}
=\frac{2.18 \times 10^{6}\times Z \times Z}{3.3 \times 10^{-10} \times n \times n^{2}}
=6.66 \times 10^{15}\left(\frac{z^{2}}{n^{3}}\right)

Schrodinger's wave equation :
\frac{\partial^{2}\psi}{\partial x^{2}} + \frac{\partial^{2}\psi}{\partial y^{2}} + \frac{\partial^{2}\psi}{\partial z^{2}} + \frac{8\pi^{2}m}{h^{2}} \left(E - V\right)\psi = 0
m = mass of electron
h = planck's constant
V = potential energy
E = Total energy
\frac{\partial}{\partial x} + \frac{\partial}{\partial y } + \frac{\partial}{\partial z} = \triangledown(Laplacian operator)
\triangledown^{2}\psi = \frac{-8\pi^{2}m}{h^{2}}\left(E - V\right)\psi

No.of radial nodes :
n − l − 1
for s = n − 1
for p = n − 2
for d = n − 3
for f = n − 4

No. of angular nodes = ' l '

Total nodes = n − 1

View the Topic in this Video from 15:20 to 37:25

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1. (n - l - 1) = radial node
2. (l) = angular node
3. (n - 1) = total nodes