Chapter 4, Problem 44P

(a)

Interpretation Introduction

Interpretation:

The shape of the wave function ${\stackrel{\sim }{\psi }}_{222}(\stackrel{\sim }{x},\stackrel{}{\stackrel{\sim }{y},\stackrel{\sim }{z}})$ in a cut plane at $\stackrel{\sim }{x}$ = 0.5 should be described.

Concept introduction:

The function which describes the position of an electron and quantum state of an isolated quantum system is known as wave function.

The general formula of the wave function for a particle in a cubic box is:

  ${\psi }_{n_x}{}_{n_y{n}_z}(x,y,z)=\sqrt{\frac{8}{L^3}}\sin \left(\frac{n_x\pi x}{L}\right)\sin \left(\frac{n_y\pi y}{L}\right)\sin \left(\frac{n_z\pi z}{L}\right)$

Where, ${\psi }_{n_x}{}_{n_y{n}_z}(x,y,z)$ is wave function and $n_x,n_y,n_z$ have values 1, 2, 3 etc.

L = length of the box.

The nodes that lie along straight lines are known as nodal lines. The point in space around the nucleus where the probability of finding electron is zero is known as nodes.

(b)

Interpretation Introduction

Interpretation:

The shape of the wave function ${\stackrel{\sim }{\psi }}_{222}(\stackrel{\sim }{x},\stackrel{}{\stackrel{\sim }{y},\stackrel{\sim }{z}})$ in a cut plane at $\stackrel{\sim }{y}$ = 0.5 should be described.

Concept introduction:

The function which describes the position of an electron and quantum state of an isolated quantum system is known as wave function.

The general formula of the wave function for a particle in a cubic box is:

  ${\psi }_{n_x}{}_{n_y{n}_z}(x,y,z)=\sqrt{\frac{8}{L^3}}\sin \left(\frac{n_x\pi x}{L}\right)\sin \left(\frac{n_y\pi y}{L}\right)\sin \left(\frac{n_z\pi z}{L}\right)$

Where, ${\psi }_{n_x}{}_{n_y{n}_z}(x,y,z)$ is wave function and $n_x,n_y,n_z$ have values 1, 2, 3 etc.

L = length of the box.

The nodes that lie along straight lines are known as nodal lines. The point in space around the nucleus where the probability of finding electron is zero is known as nodes.