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ATOMIC AND MOLECULAR SPECTRA

Atomic spectra

Emission line & adsorption line

Atomic spectral lines are of two types:

An emission line is formed when an electron makes a transition from a particular discrete energy level of an atom, to a lower energy state, emitting a photon of a particular energy and wavelength. A spectrum of many such photons will show an emission spike at the wavelength associated with these photons.

An absorption line is formed when an electron makes a transition from a lower to a higher discrete energy state, with a photon being absorbed in the process. These absorbed photons generally come from background continuum radiation and a spectrum will show a drop in the continuum radiation at the wavelength associated with the absorbed photons.

l  If the energy of the atom or molecules is confined to discrete values, for then energy can be discarded or absorbed only in discrete amounts

l  

If the energy of an atom decreases by DE, the energy is carried away as radiation of frequency                        and a line appears in the spectrum

l  The atomic and molecular spectra are evidence for the quantization of energy that observed from the frequencies of radiation absorbed and emitted by atoms and molecules.

l  Emitted or absorbed radiation appear at a series of discrete frequencies

JOHANN BALMER, 1885

l  Pattern in the wavelengths or frequencies of the lines in the atomic hydrogen spectrum

l  

Balmer showed that a plot of the frequency of the lines versus 1/n² is a linear plot

Formula Balmer

 

A plot of frequency versus 1/n² (n=3,4,5,…) for the series of lines of the hydrogen atom spectrum that occurs in the visible and near UV regions

Example:

Using Balmer’s formula, calculate the wavelength of the first few lines of the visible region of the hydrogen atomic spectrum and compare them to the experimental values

Solution:

The first line is obtained by setting n = 3, in which the case we have

The next line is obtained by setting n=4, and so

                                               

Thus, we see that the agreement with the experimental data

BALMER SERIES

Emission spectrum of the hydrogen atom in visible and the near UV region

The Rydberg formula account for all the lines in the hydrogen atomic spectrum

 All the lines in the hydrogen atomic spectrum was accounted for by generalising the Balmer formula

n₁ dan n₂ are integers but n₂ is always greater than n₁

Rydberg formula

Rydberg constant (R_H)

Name	n1	N2	Region of electromagnetic spectrum
Lyman	1	2,3,4…	UV
Balmer	2	3,4,5…	Visible
Paschen	3	4,5,6…	Near IR
Bracket	4	5,6,7…	IR
Pfund	5	6,7,8…	Far IR

The first series of lines making up the hydrogen atomic spectru

Question

Calculate the wavelength of the second line in the Paschen series and show that this lines lies in the near IR, that is , in the IR region near the visible

Solution

Angular momentum is a fundamental property of rotating system

 

Kinetic energy (in term of momentum)

Kinetic energy (in term of rotating system)

The correspondences between linear and rotating systems

Type of motion
Linear	Angular
Mass (m)	Moment of inersia (I)
Speed (v)	Angular speed
Momentum	Angular momentum
Kinetic energy	Rotational kinetic energy

The rotation of a single particle about a fixed point

Energy

Energy total = Energy kinetic + energy potential

Energy kinetics:

Energy total = Energy kinetic + energy potential

Bohr’s great contribution

Two non classical assumptions:

1. To assume the existence of stationary electron orbits
2. Assumed that the angular momentum of the electron must be quantized

The negative sign indicates that the energy states are bound states

Energies are less than when the proton and electron are infinitely separated

n=1 , the states of lowest energy (ground states energy)

Bohr frequency condition                     

                                                                                        Rydberg’s constant

                                                                                                                               

Question

Calculate R_H and compare the result to its experimental value. 109,677 cm^-1

m=9.10953x10^-31kg

e = 1.602189x10^-19C

h=6.626176x10^-34Js

C=2.99792x10⁸ms^-1

    = 8.85419x10^-12C²N^-1m^-2

Question

l  Calculate the ionization energy of the hydrogen atom

Solution:

   The ionization energy is the energy required to take the electron from the ground state to the first unbound state, which is obtained by letting n₂ = unlimited