ChaPtER 5: Spectral Lines Of Hydrogen

SCOPE OF STUDY

SUB TOPICS

Electronic

Transition in

Hydrogen Atom

Energy

Emitted and

Absorbed In A

transition

Lyman Series,

Balmer Series

and Paschen

Series

ELECTRONIC TRANSITION IN

HYDROGEN ATOMDEFINITION

Molecular electronic transitions take place

when valence electrons in a molecule are

excited from one energy level to a higher

energy level. 

ELECTRONIC TRANSITION IN

HYDROGEN ATOMscandium Sc [Ar] 3d1 4s2

titanium Ti [Ar] 3d2 4s2

vanadium V [Ar] 3d3 4s2

chromium Cr [Ar] 3d5 4s1

manganese Mn [Ar] 3d5 4s2

iron Fe [Ar] 3d6 4s2

cobalt Co [Ar] 3d7 4s2

nickel Ni [Ar] 3d8 4s2

copper Cu [Ar] 3d10 4s1

zinc Zn [Ar] 3d10 4s2

Example Of Electronic Configuration in Metals

ELECTRONIC TRANSITION IN

HYDROGEN ATOM In 1913, it was Neils Bohr who solved many of the problems at the time by

proposing that the electron revolves around the nucleus of the atom with a

definite fixed energy in a fixed path, without emitting or absorbing energy.

The electron in the hydrogen atom exists only in certain definite energy

levels.

These energy levels are called Principal Quantum Levels, denoted by the

Principal Quantum Number, n. Principal Quantum Level n = 1 is closest to the

nucleus of the atom and of lowest energy.

When the electron occupies the energy level of lowest energy the atom is

said to be in its ground state.

An atom can have only one ground state.

If the electron occupies one of the higher energy levels then the atom is in

an excited state.

An atom has many excited states.

ELECTRONIC TRANSITION IN

HYDROGEN ATOM

ENERGY EMITTED AND ABSORBED IN A

TRANSITION When a gaseous hydrogen atom in its ground state is excited by an input of

energy, its electron is 'promoted' from the lowest energy level to one of higher

energy.

The atom does not remain excited but re-emits energy as electromagnetic

radiation.

This is as a result of an electron 'falling' from a higher energy level to one of

lower energy.

This electron transition results in the release of a photon from the atom of

an amount of energy (E = hn) equal to the difference in energy of the electronic

energy levels involved in the transition.

In a sample of gaseous hydrogen where there are many trillions of atoms all

of the possible electron transitions from higher to lower energy levels will take

place many times.

A prism can now be used to separate the emitted electromagnetic radiation

into its component frequencies (wavelengths or energies).

These are then represented as spectral lines along an increasing frequency

scale to form an atomic emission spectrum.

ENERGY EMITTED AND ABSORBED IN A

TRANSITION

ENERGY EMITTED AND ABSORBED IN A

TRANSITIONA hydrogen atom in its Ground State.

The electron occupies the lowest

possible energy level which in the

case of hydrogen is the Principal

Quantum Level n = 1.

ENERGY EMITTED AND ABSORBED IN A

TRANSITION The Bohr theory was a marvellous success in explaining the spectrum of the

hydrogen atom.

His calculated wavelengths agreed perfectly with the experimentally measured

wavelengths of the spectral lines.

More recent theories about the electronic structure of atoms have refined these ideas,

but Bohr's 'model' is still very helpful to us.

For clarity, it is normal to consider electron transitions from higher energy levels to

the same Principal Quantum Level.

The diagram below illustrates the formation of a series of spectral lines in the visible

region of the spectrum of electromagnetic radiation for hydrogen, called the Balmer

Series.

ENERGY EMITTED AND ABSORBED IN A

TRANSITION

ENERGY EMITTED AND ABSORBED IN A

TRANSITION The Bohr model for an electron transition in hydrogen

between quantized energy levels with different quantum numbers

n yields a photon by emission with quantum energy:

ENERGY EMITTED AND ABSORBED IN A

TRANSITION This is often expressed in terms of the inverse wavelength or "wave

number" as follows:

Hydrogen Spectrum

LYMAN SERIES, BALMER SERIES & PASCHEN SERIES As referred to above for hydrogen atoms, electron transitions form higher energy

levels all to the n = 2 level produce a series of lines in the visible region of the

electromagnetic spectrum, called the Balmer Series.

The series of lines in the ultra-violet region, called the Lyman Series, are due to

electron transitions from higher energy levels all to the n = 1 level, and these were

discovered after Bohr predicted their existence.

LYMAN SERIES, BALMER SERIES & PASCHEN SERIES

Energy-level diagram below for the hydrogen atom, showing the transitions for

the spectral lines of the Lyman, Balmer, and Paschen series. Each vertical arrow

represents an atomic transition that gives rise to the photons of one spectral line

(a single wavelength or frequency).

Within each series, the spectral lines get closer together with increasing

frequency.

This suggests that the electronic energy levels get closer the more distant they

become from the nucleus of the atom.

No two elements have the same atomic emission spectrum; the atomic emission

spectrum of an element is like a fingerprint.

LYMAN SERIES, BALMER SERIES & PASCHEN

SERIES

LYMAN SERIES, BALMER SERIES & PASCHEN SERIES

LYMAN SERIES, BALMER SERIES & PASCHEN SERIES

Wavelength(nm)

Relative Intensity Transition Color

383.5384 5 9 -> 2 Violet

388.9049 6 8 -> 2 Violet

397.0072 8 7 -> 2 Violet

410.174 15 6 -> 2 Violet

434.047 30 5 -> 2 Violet

486.133 80 4 -> 2 Bluegreen (cyan)

656.272 120 3 -> 2 Red

656.2852 180 3 -> 2 Red

The measured lines of the Balmer series of hydrogen in the nominal visible regionare:

The measured lines of the Balmer series of hydrogen in the nominal visible region are:

LYMAN SERIES, BALMER SERIES & PASCHEN SERIESExample : Wavelength of a Lyman line.

Use this figure to determine the wavelength of the first

Lyman line, the transition from n = 2 to n = 1. In what

region of the electromagnetic spectrum does this lie?

Solution:

The energy is the difference between the two

levels, 10.2 eV. Then λ = hc/E = 1.22 x 10-7 m.

This is an ultraviolet photon.

LYMAN SERIES, BALMER SERIES & PASCHEN SERIES

Example : Wavelength of a Balmer line.

Determine the wavelength of light emitted when a hydrogen atom makes a

transition from the n = 6 to the n = 2 energy level according to the Bohr

model.

Solution:

Using equation, we find λ = 4.10 x 10-7 nm (violet).

THE END …..

“if A is success in life, then A=x+y+z; Work

= x; y = play; and z = keeping your mouth

shut” Einstein.