Phy 310 chapter 4

Dr Ahmad Taufek Abdul RahmanSchool of Physics & Material Studies

Faculty of Applied Sciences

Universiti Teknologi MARA Malaysia

Campus of Negeri Sembilan

72000 Kuala Pilah, NS

CHAPTER 4:

ATOMIC STRUCTURE

AND

ENERGY LEVELS IN AN ATOM

Application of Quantum Mechanics to

Atomic PhysicsA large portion of the chapter focuses on the hydrogen atom.

Reasons for the importance of the hydrogen atom include.

The hydrogen atom is the only atomic system that can be solved exactly.

Much of what was learned in the twentieth century about the hydrogen atom,

with its single electron, can be extended to such single-electron ions as He+

and Li2+.

The hydrogen atom is an ideal system for performing precision tests of theory

against experiment.

Also for improving our understanding of atomic structure.

The quantum numbers that are used to characterize the allowed states ofhydrogen can also be used to investigate more complex atoms.

This allows us to understand the periodic table.

The basic ideas about atomic structure must be well understood before weattempt to deal with the complexities of molecular structures and the electronicstructure of solids.

DR.ATAR @ UiTM.NS 2

PHY310: Atomic Structure and Energy

Levels in an Atom

Other Ideas in Atomic Physics

The full mathematical solution of the Schrödinger equation applied to the hydrogen

atom gives a complete and beautiful description of the atom’s properties.

Quantum numbers are used to characterize various allowed states in the atom.

The quantum numbers have physical significance.

Certain quantum states are affected by a magnetic field.

The exclusion principle is important for understanding the properties of multielectron

atoms and the arrangement of the elements in the periodic table.

DR.ATAR @ UiTM.NS 3


Levels in an Atom

Atomic Spectra

All objects emit thermal radiation characterized by a continuous distribution of

wavelengths.

A discrete line spectrum is observed when a low-pressure gas is subjected to an

electric discharge.

Observation and analysis of these spectral lines is called emission spectroscopy.

The simplest line spectrum is that for atomic hydrogen.

DR.ATAR @ UiTM.NS 4


Levels in an Atom

Emission Spectra Examples

DR.ATAR @ UiTM.NS 5


Levels in an Atom

Uniqueness of Atomic Spectra

Other atoms exhibit completely different line spectra.

Because no two elements have the same line spectrum, the phenomena represents a

practical and sensitive technique for identifying the elements present in unknown

samples.

DR.ATAR @ UiTM.NS 6


Levels in an Atom

Absorption Spectroscopy

An absorption spectrum is obtained by passing white light from a continuous source

through a gas or a dilute solution of the element being analyzed.

The absorption spectrum consists of a series of dark lines superimposed on the

continuous spectrum of the light source.

DR.ATAR @ UiTM.NS 7


Levels in an Atom

Balmer Series

In 1885, Johann Balmer found an

empirical equation that correctly predicted

the four visible emission lines of

hydrogen.

Hα is red, λ = 656.3 nm

Hβ is green, λ = 486.1 nm

Hγ is blue, λ = 434.1 nm

Hδ is violet, λ = 410.2 nm

DR.ATAR @ UiTM.NS 8


Levels in an Atom

Emission Spectrum of Hydrogen –

Equation The wavelengths of hydrogen’s spectral lines can be found from

RH is the Rydberg constant

RH = 1.097 373 2 x 107 m-1

n is an integer, n = 3, 4, 5,…

The spectral lines correspond to different values of n.

Values of n from 3 to 6 give the four visible lines.

Values of n > 6 give the ultraviolet lines in the Balmer series.

The series limit is the shortest wavelength in the series and corresponds to n →∞.

H 2 2

1 1 1

2R

λ n

DR.ATAR @ UiTM.NS 9


Levels in an Atom

Other Hydrogen Series

Other series were also discovered and their wavelengths can be calculated:

Lyman series:

Paschen series:

Brackett series:

H 2

1 11 2 3 4, , ,R n

λ n

H 2 2

1 1 14 5 6

3, , ,R n

λ n

H 2 2

1 1 15 6 7

4, , ,R n

λ n

DR.ATAR @ UiTM.NS 10


Levels in an Atom

Joseph John Thomson

1856 – 1940

English physicist

Received Nobel Prize in 1906

Usually considered the discoverer of the

electron

Worked with the deflection of cathode

rays in an electric field

Opened up the field of subatomic

particles



Levels in an Atom

Early Models of the Atom,

Thomson’sJ. J. Thomson established the charge to

mass ratio for electrons.

His model of the atom

A volume of positive charge

Electrons embedded throughout

the volume

The atom as a whole would be

electrically neutral.



Levels in an Atom

Rutherford’s Thin Foil Experiment

Experiments done in 1911

A beam of positively charged alpha

particles hit and are scattered from a thin

foil target.

Large deflections could not be explained

by Thomson’s model.



Levels in an Atom

Early Models of the Atom,

Rutherford’sRutherford

Planetary model

Based on results of thin foil

experiments

Positive charge is concentrated

in the center of the atom, called

the nucleus

Electrons orbit the nucleus like

planets orbit the sun



Levels in an Atom

Difficulties with the Rutherford Model

Atoms emit certain discrete characteristic frequencies of electromagnetic radiation.

The Rutherford model is unable to explain this phenomena.

Rutherford’s electrons are undergoing a centripetal acceleration.

It should radiate electromagnetic waves of the same frequency.

The radius should steadily decrease as this radiation is given off.

The electron should eventually spiral into the nucleus.

It doesn’t



Levels in an Atom

Niels Bohr

1885 – 1962

Danish physicist

An active participant in the early

development of quantum mechanics

Headed the Institute for Advanced

Studies in Copenhagen

Awarded the 1922 Nobel Prize in physics

For structure of atoms and the

radiation emanating from them



Levels in an Atom

The Bohr Theory of Hydrogen

In 1913 Bohr provided an explanation of atomic spectra that includes some features

of the currently accepted theory.

His model includes both classical and non-classical ideas.

He applied Planck’s ideas of quantized energy levels to Rutherford’s orbiting

electrons.

This model is now considered obsolete.

It has been replaced by a probabilistic quantum-mechanical theory.

The model can still be used to develop ideas of energy quantization and angular

momentum quantization as applied to atomic-sized systems.



Levels in an Atom

Bohr’s Postulates for Hydrogen, 1

The electron moves in circular orbits

around the proton under the electric force

of attraction.

The Coulomb force produces the

centripetal acceleration.



Levels in an Atom

Bohr’s Postulates, 2

Only certain electron orbits are stable.

Bohr called these stationary states.

These are the orbits in which the atom does not emit energy in the form ofelectromagnetic radiation, even though it is accelerating.

Therefore, the energy of the atom remains constant and classical mechanicscan be used to describe the electron’s motion.

This representation claims the centripetally accelerated electron does notcontinuously emit energy and therefore does not eventually spiral into thenucleus.



Levels in an Atom


Radiation is emitted by the atom when the electron makes a transition from a moreenergetic initial stationary state to a lower-energy stationary state.

The transition cannot be treated classically.

The frequency emitted in the transition is related to the change in the atom’senergy.

The frequency is independent of frequency of the electron’s orbital motion.

The frequency of the emitted radiation is given by

Ei – Ef = hƒ

If a photon is absorbed, the electron moves to ahigher energy level.



Levels in an Atom


The size of the allowed electron orbits is determined by a condition imposed on the

electron’s orbital angular momentum.

The allowed orbits are those for which the electron’s orbital angular momentum about

the nucleus is quantized and equal to an integral multiple of h



Levels in an Atom

Bohr’s Postulates, Notes

These postulates were a mixture of established principles and completely new ideas.

Postulate 1 – from classical mechanics

Treats the electron in orbit around the nucleus in the same way we treat a

planet in orbit around a star.

Postulate 2 – new idea

It was completely at odds with the understanding of electromagnetism at the

time.

Postulate 3 – Principle of Conservation of Energy

Postulate 4 – new idea

Had no basis in classical physics



Levels in an Atom

Mathematics of Bohr’s Assumptions

and ResultsElectron’s orbital angular momentum

mevr = nħ where n = 1, 2, 3,…

The total energy of the atom is

The electron is modeled as a particle in uniform circular motion, so the electrical force

on the electron equals the product of its mass and its centripetal acceleration.

The total energy can also be expressed as .

The total energy is negative, indicating a bound electron-proton system.

221

2e e

eE K U m v k

r

2

2ek e

Er



Levels in an Atom

Bohr Radius

The radii of the Bohr orbits are quantized

This shows that the radii of the allowed orbits have discrete values—they are

quantized.

This result is based on the assumption that the electron can exist only in

certain allowed orbits determined by n (Bohr’s postulate 4).

When n = 1, the orbit has the smallest radius, called the

Bohr radius, ao

ao = 0.052 9 nm

2 2

21 2 3, , ,n

e e

nr n

m k e



Levels in an Atom

Radii and Energy of Orbits

A general expression for the radius of any orbit in a hydrogen atom is

rn = n2ao

The energy of any orbit is

This becomes En = - 13.606 eV / n2

2

2

11 2 3,

2, ,e

n

o

k eE n

a n



Levels in an Atom

Specific Energy Levels

Only energies satisfying the energy equation are allowed.

The lowest energy state is called the ground state.

This corresponds to n = 1 with E = –13.606 eV

The ionization energy is the energy needed to completely remove the electron from

the ground state in the atom.

The ionization energy for hydrogen is 13.6 eV.



Levels in an Atom

Energy Level Diagram

Quantum numbers are given on the left

and energies on the right.

The uppermost level, E = 0, represents

the state for which the electron is

removed from the atom.

Adding more energy than this

amount ionizes the atom.



Levels in an Atom

Frequency and Wavelength of Emitted

PhotonsThe frequency of the photon emitted when the electron makes a transition from an

outer orbit to an inner orbit is

It is convenient to look at the wavelength instead.

The wavelengths are found by

The value of RH from Bohr’s analysis is in excellent agreement with the experimental

value.

2

2 2

1 1

2ƒ i f e

o f i

E E k e

h a h n n

2

2 2 2 2

1 1 1 1 1

2

ƒ eH

o f i f i

k eR

λ c a hc n n n n



Levels in an Atom

Extension to Other Atoms

Bohr extended his model for hydrogen to other elements in which all but one electron had been removed.

Z is the atomic number of the element and is the number of protons in the nucleus.

2

2 2

21 2 3

2, , ,

on

en

o

ar n

Z

k e ZE n

a n



Levels in an Atom

Difficulties with the Bohr Model

Improved spectroscopic techniques found that many of the spectral lines of hydrogen

were not single lines.

Each ―line‖ was actually a group of lines spaced very close together.

Certain single spectral lines split into three closely spaced lines when the atoms were

placed in a magnetic field.

The Bohr model cannot account for the spectra of more complex atoms.

Scattering experiments show that the electron in a hydrogen atom does not move in a

flat circle, but rather that the atom is spherical.

The ground-state angular momentum of the atom is zero.

These deviations from the model led to modifications in the theory and ultimately to a

replacement theory.



Levels in an Atom

Bohr’s Correspondence Principle

Bohr’s correspondence principle states that quantum physics agrees with classical

physics when the differences between quantized levels become vanishingly small.

Similar to having Newtonian mechanics be a special case of relativistic

mechanics when v << c.



Levels in an Atom

The Quantum Model of the Hydrogen

AtomThe difficulties with the Bohr model are removed when a full quantum model involving

the Schrödinger equation is used to describe the hydrogen atom.

The potential energy function for the hydrogen atom is

ke is the Coulomb constant

r is the radial distance from the proton to the electron

The proton is situated at r = 0

2

( ) e

eU r k

r



Levels in an Atom

Quantum Model, cont.

The formal procedure to solve the hydrogen atom is to substitute U(r) into the

Schrödinger equation, find the appropriate solutions to the equations, and apply

boundary conditions.

Because it is a three-dimensional problem, it is easier to solve if the rectangular

coordinates are converted to spherical polar coordinates.



Levels in an Atom

Quantum Model, final

ψ(x, y, z) is converted to ψ(r, θ, φ)

Then, the space variables can be

separated:

ψ(r, θ, φ) = R(r), ƒ(θ), g(φ)

When the full set of boundary conditions

are applied, we are led to three different

quantum numbers for each allowed state.

The three different quantum numbers are

restricted to integer values.

They correspond to three degrees of

freedom.

Three space dimensions



Levels in an Atom

Principal Quantum Number

The first quantum number is associated with the radial function R(r).

It is called the principal quantum number.

It is symbolized by n.

The potential energy function depends only on the radial coordinate r.

The energies of the allowed states in the hydrogen atom are the same En values

found from the Bohr theory.



Levels in an Atom

Orbital and Orbital Magnetic Quantum

NumbersThe orbital quantum number is symbolized by ℓ.

It is associated with the orbital angular momentum of the electron.

It is an integer.

The orbital magnetic quantum number is symbolized by mℓ.

It is also associated with the angular orbital momentum of the electron and is

an integer.



Levels in an Atom

Quantum Numbers, Summary of

Allowed ValuesThe values of n are integers that can range from 1 to

The values of ℓ are integers that can range from 0 to n - 1.

The values of mℓ are integers that can range from –ℓ to ℓ.

Example:

If n = 1, then only ℓ = 0 and mℓ = 0 are permitted

If n = 2, then ℓ = 0 or 1

If ℓ = 0 then mℓ = 0

If ℓ = 1 then mℓ may be –1, 0, or 1



Levels in an Atom

Quantum Numbers, Summary Table



Levels in an Atom

Shells

Historically, all states having the same principle quantum number are said to form a

shell.

Shells are identified by letters K, L, M,… for which n = 1, 2, 3, …

All states having the same values of n and ℓ are said to form a subshell.

The letters s, p, d, f, g, h, .. are used to designate the subshells for which ℓ = 0,

1, 2, 3,…



Levels in an Atom

Shell Notation, Summary Table



Levels in an Atom

Subshell Notation, Summary Table



Levels in an Atom

Wave Functions for Hydrogen

The simplest wave function for hydrogen is the one that describes the 1s state and is

designated ψ1s(r).

As ψ1s(r) approaches zero, r approaches and is normalized as presented.

ψ1s(r) is also spherically symmetric

This symmetry exists for all s states.

1

3

1( ) or a

s

o

ψ r eπa



Levels in an Atom

Probability Density

The probability density for the 1s state is

The radial probability density function P(r) is the probability per unit radial length of

finding the electron in a spherical shell of radius r and thickness dr.

2 2

1 3

1or a

s

o

ψ eπa



Levels in an Atom

Radial Probability Density

A spherical shell of radius r and thickness

dr has a volume of

4πr2 dr

The radial probability function is

P(r) = 4πr2 |ψ|2



Levels in an Atom

P(r) for 1s State of Hydrogen

The radial probability density function forthe hydrogen atom in its ground state is

The peak indicates the most probablelocation.

The peak occurs at the Bohr radius.

The average value of r for the ground

state of hydrogen is 3/2 ao.

22

1 3

4( ) or a

s

o

rP r e

a



Levels in an Atom

Electron Clouds

According to quantum mechanics, the

atom has no sharply defined boundary as

suggested by the Bohr theory.

The charge of the electron is extended

throughout a diffuse region of space,

commonly called an electron cloud.

This shows the probability density as a

function of position in the xy plane.

The darkest area, r = ao, corresponds to

the most probable region.



Levels in an Atom

Wave Function of the 2s state

The next-simplest wave function for the hydrogen atom is for the 2s state.

n = 2; ℓ = 0

The normalized wave function is

ψ2s depends only on r and is spherically symmetric.

32

2

2

1 1( ) 2

4 2or a

s

o o

rψ r e

a aπ



Levels in an Atom

Comparison of 1s and 2s States

The plot of the radial probability density

for the 2s state has two peaks.

The highest value of P corresponds to the

most probable value.

In this case, r 5ao



Levels in an Atom

Physical Interpretation of ℓ

The magnitude of the angular momentum of an electron moving in a circle of radius r

is

L = mevr

The direction of the angular momentum vector is perpendicular to the plane of the

circle.

The direction is given by the right hand rule.

In the Bohr model, the angular momentum of the electron is restricted to multiples of

.

This incorrectly predicts that the ground state of hydrogen has one unit of

angular momentum.

If L is taken to be zero in the Bohr model, the electron must be pictured as a

particle oscillating along a straight line through the nucleus.



Levels in an Atom

Physical Interpretation

of ℓ, cont.Quantum mechanics resolves these difficulties found in the Bohr model.

According to quantum mechanics, an atom in a state whose principle quantum

number is n can take on the following discrete values of the magnitude of the orbital

angular momentum:

L can equal zero, which causes great difficulty when attempting to apply

classical mechanics to this system.

In the quantum mechanical representation, the electron cloud for the L = 0

state is spherically symmetric and has no fundamental rotation axis.

1 0 1 2 1L , , , , n



Levels in an Atom

Physical Interpretation of mℓ

The atom possesses an orbital angular momentum.

There is a sense of rotation of the electron around the nucleus, so that a magnetic

moment is present due to this angular momentum.

There are distinct directions allowed for the magnetic moment vector with respect to

the magnetic field vector .

Because the magnetic moment of the atom can be related to the angular

momentum vector, , the discrete direction of the magnetic moment vector translates

into the fact that the direction of the angular momentum is quantized.

Therefore, Lz, the projection of along the z axis, can have only discrete values.

μ

L

L



Levels in an Atom

Physical Interpretation of mℓ, cont.

The orbital magnetic quantum number mℓ specifies the allowed values of the z

component of orbital angular momentum.

Lz = mℓ

The quantization of the possible orientations of with respect to an external

magnetic field is often referred to as space quantization.

does not point in a specific direction

Even though its z-component is fixed

Knowing all the components is inconsistent with the uncertainty principle

Imagine that must lie anywhere on the surface of a cone that makes an angle θ

with the z axis.

L

L

L



Levels in an Atom

Physical Interpretation of mℓ, final

θ is also quantized

Its values are specified through

cos

1

zL mθ

L



Levels in an Atom

Zeeman Effect

The Zeeman effect is the splitting of

spectral lines in a strong magnetic field.

In this case the upper level, with ℓ = 1,

splits into three different levels

corresponding to the three different

directions of µ.



Levels in an Atom

Spin Quantum Number ms

Electron spin does not come from the Schrödinger equation.

Additional quantum states can be explained by requiring a fourth quantum number for

each state.

This fourth quantum number is the spin magnetic quantum number ms.



Levels in an Atom

Electron Spins

Only two directions exist for electron

spins.

The electron can have spin up (a) or spin

down (b).

In the presence of a magnetic field, the

energy of the electron is slightly different

for the two spin directions and this

produces doublets in spectra of certain

gases.



Levels in an Atom

Electron Spins, cont.

The concept of a spinning electron is conceptually useful.

The electron is a point particle, without any spatial extent.

Therefore the electron cannot be considered to be actually spinning.

The experimental evidence supports the electron having some intrinsic angularmomentum that can be described by ms.

Dirac showed this results from the relativistic properties of the electron.



Levels in an Atom

Spin Angular Momentum

The total angular momentum of a particular electron state contains both an orbital

contribution and a spin contribution.

Electron spin can be described by a single quantum number s, whose value can only

be s = ½ .

The spin angular momentum of the electron never changes.

The magnitude of the spin angular momentum is

The spin angular momentum can have two orientations relative to a z axis, specified

by the spin quantum number ms = ± ½ .

ms = + ½ corresponds to the spin up case.

ms = - ½ corresponds to the spin down case.

S

L

3( 1)

2S s s



Levels in an Atom

Spin Angular Momentum, cont.

The z component of spin angular

momentum is Sz = msh = ± ½ h

Spin angular moment is quantized.



Levels in an Atom

Spin Magnetic Moment

The spin magnetic moment µspin is related to the spin angular momentum by

The z component of the spin magnetic moment can have values

Sspin

e

eμ

m

spin2

,z

e

eμ

m



Levels in an Atom

Quantum States

There are eight quantum states corresponding to n = 2.

These states depend on the addition of the possible values of ms.

Table 42.4 summarizes these states.



Levels in an Atom

Quantum Numbers for n = 2 State of

Hydrogen



Levels in an Atom

Wolfgang Pauli

1900 – 1958

Austrian physicist

Important review article on relativity

At age 21Discovery of the exclusion principle

Explanation of the connection betweenparticle spin and statistics

Relativistic quantum electrodynamics

Neutrino hypothesis

Hypotheses of nuclear spin



Levels in an Atom

The Exclusion Principle

The four quantum numbers discussed so far can be used to describe all the electronic

states of an atom regardless of the number of electrons in its structure.

The exclusion principle states that no two electrons can ever be in the same

quantum state.

Therefore, no two electrons in the same atom can have the same set of

quantum numbers.

If the exclusion principle was not valid, an atom could radiate energy until every

electron was in the lowest possible energy state and the chemical nature of the

elements would be modified.



Levels in an Atom

Filling Subshells

The electronic structure of complex atoms can be viewed as a succession of filled

levels increasing in energy.

Once a subshell is filled, the next electron goes into the lowest-energy vacant state.

If the atom were not in the lowest-energy state available to it, it would radiate

energy until it reached this state.



Levels in an Atom

Orbitals

An orbital is defined as the atomic state characterized by the quantum numbers n, ℓ

and mℓ.

From the exclusion principle, it can be seen that only two electrons can be present in

any orbital.

One electron will have spin up and one spin down.

Each orbital is limited to two electrons, the number of electrons that can occupy the

various shells is also limited.



Levels in an Atom

Allowed Quantum States, Example

with n = 3

In general, each shell can accommodate up to 2n2 electrons.



Levels in an Atom

Hund’s Rule

Hund’s Rule states that when an atom has orbitals of equal energy, the order in which

they are filled by electrons is such that a maximum number of electrons have

unpaired spins.

Some exceptions to the rule occur in elements having subshells that are close

to being filled or half-filled.



Levels in an Atom

Configuration of Some Electron States

The filling of electron

states must obey both

the exclusion principle

and Hund’s rule.



Levels in an Atom

Periodic Table

Dmitri Mendeleev made an early attempt at finding some order among the chemical

elements.

He arranged the elements according to their atomic masses and chemical similarities.

The first table contained many blank spaces and he stated that the gaps were there

only because the elements had not yet been discovered.

By noting the columns in which some missing elements should be located, he was

able to make rough predictions about their chemical properties.

Within 20 years of the predictions, most of the elements were discovered.

The elements in the periodic table are arranged so that all those in a column have

similar chemical properties.



Levels in an Atom

Periodic Table, Explained

The chemical behavior of an element depends on the outermost shell that contains

electrons.

For example, the inert (or noble) gases (last column) have filled subshells and a wide

energy gap occurs between the filled shell and the next available shell.



Levels in an Atom

Hydrogen Energy Level Diagram

RevisitedThe allowed values of ℓ are separated

horizontally.

Transitions in which ℓ does not change

are very unlikely to occur and are called

forbidden transitions.

Such transitions actually can

occur, but their probability is very

low compared to allowed

transitions.



Levels in an Atom

Selection Rules

The selection rules for allowed transitions are

Δℓ = ±1

Δmℓ = 0, ±1

The angular momentum of the atom-photon system must be conserved.

Therefore, the photon involved in the process must carry angular momentum.

The photon has angular momentum equivalent to that of a particle with spin 1.

A photon has energy, linear momentum and angular momentum.



Levels in an Atom

Multielectron Atoms

For multielectron atoms, the positive nuclear charge Ze is largely shielded by thenegative charge of the inner shell electrons.

The outer electrons interact with a net charge that is smaller than the nuclearcharge.

Allowed energies are

Zeff depends on n and ℓ

.

2

eff

2

136n

eV ZE

n



Levels in an Atom

X-Ray Spectra

These x-rays are a result of the slowing

down of high energy electrons as they

strike a metal target.

The kinetic energy lost can be anywhere

from 0 to all of the kinetic energy of the

electron.

The continuous spectrum is called

bremsstrahlung, the German word for

―braking radiation‖.



Levels in an Atom

X-Ray Spectra, cont.

The discrete lines are called characteristic x-rays.

These are created when

A bombarding electron collides with a target atom.

The electron removes an inner-shell electron from orbit.

An electron from a higher orbit drops down to fill the vacancy.

The photon emitted during this transition has an energy equal to the energy difference

between the levels.

Typically, the energy is greater than 1000 eV.

The emitted photons have wavelengths in the range of 0.01 nm to 1 nm.



Levels in an Atom

Moseley Plot

Henry G. J. Moseley plotted the values of

atoms as shown.

λ is the wavelength of the Kα line of each

element.

The Kα line refers to the photon

emitted when an electron falls

from the L to the K shell.

From this plot, Moseley developed a

periodic table in agreement with the one

based on chemical properties.



Levels in an Atom

Stimulated Absorption

When a photon has energy hƒ equal tothe difference in energy levels, it can beabsorbed by the atom.

This is called stimulated absorptionbecause the photon stimulates the atomto make the upward transition.

At ordinary temperatures, most of theatoms in a sample are in the groundstate.

The absorption of the photon causessome of the atoms to be raised to excitedstates.



Levels in an Atom

Spontaneous Emission

Once an atom is in an excited state, theexcited atom can make a transition to alower energy level.

This process is known as spontaneousemission.

Because it happens naturally



Levels in an Atom

Stimulated Emission

In addition to spontaneous emission,

stimulated emission occurs.

Stimulated emission may occur when the

excited state is a metastable state.

A metastable state is a state whose

lifetime is much longer than the typical 10-

8 s.

An incident photon can cause the atom to

return to the ground state without being

absorbed.

Therefore, you have two photons withidentical energy, the emitted photon andthe incident photon.

They both are in phase and travel in the samedirection.



Levels in an Atom

Lasers – Properties of Laser Light

Laser light is coherent.

The individual rays in a laser beam maintain a fixed phase relationship with

each other.

Laser light is monochromatic.

The light has a very narrow range of wavelengths.

Laser light has a small angle of divergence.

The beam spreads out very little, even over long distances.



Levels in an Atom

Lasers – Operation

It is equally probable that an incident photon would cause atomic transitions upward

or downward.

Stimulated absorption or stimulated emission

If a situation can be caused where there are more electrons in excited states than in

the ground state, a net emission of photons can result.

This condition is called population inversion.

The photons can stimulate other atoms to emit photons in a chain of similar

processes.

The many photons produced in this manner are the source of the intense, coherent

light in a laser.



Levels in an Atom

Conditions for Build-Up of Photons

The system must be in a state of population inversion.

The excited state of the system must be a metastable state.

In this case, the population inversion can be established and stimulatedemission is likely to occur before spontaneous emission.

The emitted photons must be confined in the system long enough to enable them tostimulate further emission.

This is achieved by using reflecting mirrors.



Levels in an Atom

Laser Design – Schematic



Levels in an Atom

Energy-Level Diagram for Neon in

a Helium-Neon LaserThe atoms emit 632.8-nm photons

through stimulated emission.

The transition is E3* to E2

* indicates a metastable state



Levels in an Atom

Laser Applications

Applications include:

Medical and surgical procedures

Precision surveying and length measurements

Precision cutting of metals and other materials

Telephone communications

Biological and medical research



Levels in an Atom

Phy 310 chapter 4

Technology

Transcript of Phy 310 chapter 4