Chapter 5, Problem 5.134CP

Interpretation Introduction

Interpretation:

‘change of energy’ should be identified.

Concept introduction:

From the Bohr postulates the radius of an orbit and its energy can be determined but to explain the atomic spectra the orbital concept have to introduce. The energy gap between the successive orbitals can be determined from the energy expression and the corresponding energy needed to excite an electron from a particular orbital to other orbital give rise the wave numbers which is associated with some particular spectrum. In the figure it is shown n = 1 to infinity.

The electron jumps from n=1 to n=2 is called the 1^st excitation and n=2 to n=3 is 2^nd excitation and like that. It is seen that as the number of n increases the energy gap between the successive orbitals decreases. The energy required to jump one electron from n=1 to n= infinity is called the ionisation energy of the atom.

Given:

In the Bohr model of atomic structure, electrons are constrained to orbit a nucleus at specific distances given by the equation, $r=\frac{n^2{a}_0}{Z}$.

Where r = radius of the orbit, Z is the charge of the nucleus and $a_0$ is the Bohr radius and has the value of $5.292\times {10}^{-11}$ m, and n is a positive integer (n = 1, 2 ,3, ……..) like a principal quantum number.
Bohr also concluded the energy level E of an electron in a given orbit is $E=\frac{-Z{e}^2}{2r}$ , Where e is the charge of an electron.

To determine:

The difference of energy i.e. $\Delta E$ between the two successive energy levels.
The relation of the derived equation with the Balmer-Rydberg equation.