Chapter 8, Problem 106IAE

Interpretation Introduction

Interpretation:

Whether the value of n equals to 138 is a bound state or not needs to be determined. If yes, the sort of state needs to be explained. Also, the radius of the orbit and number of revolutions taken by electron per second around the nucleus needs to be determined.

Concept introduction:

Bound state is defined as a quantum state of particle which is special as the particle in this state remains localized in one or more space regions.

There may be external potential or due to another particle. If potential is due to the presence of another particle, a bound state is defined as a state that represents 2 or more particles having interaction energy more than the total energy of particles.

The radius of the orbit can be calculated using the following relation:

$r_n=\frac{n^2{h}^2}{4{\pi }^{2}mZ{e}^2}$

Here, n is principle quantum number, Z is atomic number, h is Planck’s constant, m is mass of electron and e is charge on electron.

The revolutions make by the electrons around the nucleus can be calculated as follows:

$\omega =\frac{nh}{2\pi m{r}^2}$

Here, n is principle quantum number, h is Planck’s constant, m is mass of electron and r is radius of the orbit.