1. structure of the atom (1)

8/19/2019 1. Structure of the Atom (1)

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SACE Stage 2 Physics

The Structure of The

Atom


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Emission Spectra

Can be observed when a material (gas) glows by heating or an electric

current is passed through it.

Only particular frequencies of light are emitted.

(a) individual wavelengths observed. Show up as line images (interference

maima) of the slit in the spectrometer.

(b) the pattern is characterised by the type of material doing the emitting eg.

!a" !e" #" $g all produce different spectra. %sed to identify elements byelectric discharge through a gas (or vapour of the element) at low

pressure and eamining the spectra produced via diffraction

spectrometer.

(c) intensity (ie brightness) of spectral lines for a given element not same.

The number of lines present is dependent on temperature (higher T"

more lines).


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Diffraction Spectrometer

&ight source

Collimator

!arrow slit

'iffraction grating

or prism

Telescope

yepiece lens

'ifferent wave lengths diffract at different angles.

$easurements taen can determine the type of gas that

produces the light.


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Diffraction Spectrometer

The diffraction grating in the spectrometer splits up the different colours. *ertical lines

are seen as the lines are simply images of the slit

A narrow slit (hence a broad diffraction pattern) is needed to avoid overlap of the lines)

+aint lines,right lines


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Energy Levels in Atoms

The presence of discretefrequencies in the

emission spectrum of an

atom" can be interpreted

as providing evidence for

the eistence of

discrete atomic energylevels which can be

shown on an energy level

diagram.


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Single atoms only emit discrete frequencies ⇒ implies that the atoms canonly have discrete energy levels.


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-hen an atom is raised to an energy level with n/ it is said to be

excited and it can return to a lower energy level in the process of theatom emitting one or more different frequency photons.


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The ionisation energy (or binding energy) of an atom is defined as the

minimum energy that must be absorbed by an atom in its ground state to

cause ionisation. 0t is the energy necessary to remove the most looselybound electron.

eg. ionisation energy for # is /1.23e*


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4utherford deduced that most of the mass of an atom was concentrated in

a small region (diameter about /56/7m) and called it the nucleus. The

electrons (charge e and mass me) eisted outside of the nucleus.

Atomic diameter found to be about /56/5m.

Atoms are mostly space.


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The charge on any atomic nucleus is 89 e (e : magnitude of electron

charge) and where"

9 : atomic number

: number of electrons in a neutral atom

: position of atom (element) in periodic table.


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Spectrum of Atomic Hydrogen

;ossible energy leveltransitions that enable

photons to be emitted

from atomic

hydrogen.


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-hen the transitions

occur to the ground state

(n : /) the minimumenergy of a photon

emitted<

nm

m

E

hc

hchf E Since

J

eV

hf E E E mn

120

102.1

106.12.10

1031063.6

106.12.10

2.104.36.13

7

19

834

19

=

×=

××

×××=

∆=

==

××=

=−

=−=∆

−

−

−

−

λ

λ


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The Lyman series consists of all lines involving a transition to state n : /

from a state n /. These are %* lines.

The Balmer series consists of all lines from n = to n : = (the first ecited

state). Some of these are visible but the series limit is in the %*.

The Paschen series consists of all lines from n 1 to n: 1. These are less

energetic photons and the lines are in the infrared.


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Ionisation Energy

The ionisation energy of an atom is the minimum energy required to remove

a single electron from an atom in its most stable (or ground) state.

The ionisation energy for hydrogen is therefore /1.3e*

or /1.3 > /.3 > /56/? : =.= > /56/@.


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Examples

One of the spectral line of the sodium emission has a wavelength of

2?5nm. #ow much energy does the sodium lose when the photon is

emitted.


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Examples

One of the spectral line of the sodium emission has a wavelength of

2?5nm. #ow much energy does the sodium lose when the photon is

emitted.

energy.of amount samethelosesatomThe

J

hc E is photontheof energyThe

19

7

834

1037.3

109.51031063.6

−

−

−

×=

×

×××=

=λ


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Examples

Calculate the frequency and wavelength of the photon of light emitted when

an electron in hydrogen falls from the E2 level to the E level.

Hz f

Hz 101.632

f

J 101.632hf ei

J 101.632is photontheof energythe

J

J E

eV E E E changeenergyThe

1!

1!

1!

2

15

34

18

19

1

1046.2

1063.6

..

10632.1

106.12.10

2.10)6.13(4.3

×=

×

×=

×=

×∴

×=

××=∆∴

=−−−=−=∆

−

−

−


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Examples

nm

m

f

c

f c e"uation#a$e %rom

122

1022.1

1046.2

103

7

15

8

=

×=

×

×=

=

=

−

λ

λ


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Examples

Calculate the frequency of the photo emitted when an E! to E transition

occurs in hydrogen.


21/54

Examples

Calculate the frequency of the photo emitted when an E! to E transition

occurs in hydrogen.

Hz

Hz h

f

J 101.&3hf ei

J 101.&3is photontheof energythe

J J E

eV E E E changeenergyThe

1!

1!

3

15

34

18

1819

1

1091.2

1063.6

1093.1

..

1093.1106.109.12

09.12)6.13(51.1

×=

×

×==∴

×=

×∴

×=××=∆∴

=−−−=−=∆

−

−

−−

λ


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Excitation of Atoms

(/)The electron in a hydrogen atom usually eists in the lowest"

most stable energy state. ie the ground state or n: / state.

(=) nergy may be supplied to the atom as a result of collision with

another atom in a hot gas or as a result of collision with other particles

(eg electrons or alpha particles or photons). 0f the correct amount

(quanta or photon) of energy is absorbed by the atom then the electron

can Bump to an ecited state. The lifetime of these ecited states isvery short (eg /56? s).


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Excitation of Atoms

(1) The electron almost immediately is attracted bac to the ground state

emitting energy in the form of a photon or series of lower energy

photons. (This is nown as fluorescence). The frequency of the emittedphoton is given by

= 6 / : hf


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5

65.27 e*

65.@@ e*

6/.2 e*

61.7 e*

!"#$

e%

2"& e%

2" e%

#"2 e%

6/1.3 e* # e%

!"$ e%

n : /

n : =

n : 1

n : 7n : 2

n →∞

round

state

+irst ecited state

Second ecited

state

Excitation

energy

+ree states

;hoton /<

hf / : /=./ 6 /5.=

: /.? e*

;hoton =<

hf = :/5.= 6 5

: /5.= e*

;hoton 1<

hf 1 : /=./ 6 5

: /=./ e*

Hydrogen


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Excitation of Atoms

(a) the DsiEeF of the transitition (DBumpF between energy levels) determines

the energy of the photon and hence the frequency or wavelength of thelight.

(b) The number of identical DBumpsF occurring across the whole number of

atoms present (ie the probability of the Bump) determines the brightness

(intensity) of the light.

(c) Only particular frequencies will be emitted (those corresponding to

Bumps between permitted stable orbits)" hence a line emission

spectrum will be observed.


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Example

Calculate the energy of all the possible photons that could be emitted when a

hydrogen atom is ecited to the 1 level. -hat are the wavelengths of these

photons and in which region of the electromagnetic spectrum would they befoundG


27/54

Example

Calculate the energy of all the possible photons that could be emitted when a

hydrogen atom is ecited to the 1 level. -hat are the wavelengths of these

photons and in which region of the electromagnetic spectrum would they befoundG

Answer< ;ossible transition that could occur are"

⇒ 1 to /

⇒ 1 to =

⇒ = to /


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Example

+or the 1 to / transition"

$iolet'!(ultra nm

m

E

hc

hc E )sing

J

J

eV photonof Energy

eV E E E

103

1093.1

1031063.6

1093.1

106.109.12

09.12

09.12

18

834

18

19

13

=

×

×××=

=

=

×=

××=

=∴

=−=∆

−

−

−

−

λ

λ


29/54

Example

+or the 1 to = transition"

re*'$isi+lethe(in nm

m

E

hc

hc E )sing

J

J

eV photonof Energy

eV E E E

662

1002.3

1031063.6

1002.3

106.189.1

89.1

89.1

19

834

19

19

23

=

×

×××=

=

=

×=

××=

=∴

=−=∆

−

−

−

−

λ

λ


30/54

Example

+or the = to / transition"

$iolet'!(ultra nm

m

E

hc

hc E )sing

J

J

eV photonof Energy

eV E E E

125

106.1

1031063.6

106.1

106.12.10

2.10

2.10

18

834

18

19

12

=

×

×××=

=

=

×=

××=

=∴

=−=∆

−

−

−

−

λ

λ


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Continuous Spectra

A continuous spectra consists of a continuous range of frequencies that

etend from the 04 to %* range.

All bodies emit radiation" as the temperature of the body increases" the

photon energy increases.

An ordinary electric filament lamp contains a tungsten filament that can be

heated in an inert gas by the passage of electricity through the filament

wire. -hen turned on the wire heats up very quicly H first Dred hotF andthen it becomes Dwhite hotF as a larger proportion of the shorter

wavelengths are emitted.


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Continuous Spectra

2555 I

7555 I

1555 I

+requency

0ntensity

As the temperature increases" more of the longer wavelengths are emitted

producing the white light after initially appearing redish in a filament globe.


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Line A'sorption Spectrum

-hen light with a continuous spectrum is incident on a gas of an element"

discrete frequencies of light are absorbed" resulting in a line absorption

spectrum.


34/54


35/54

Line A'sorption of Atomic Hydrogen

0f a continuous array of photons is incident on hydrogen atoms (ground

state)" then photons of energy corresponding to the transition &/" &=" &1"

J."&∞ would be absorbed. Other photons will pass through.


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&ine absorption Spectrum of #ydrogen 6

&ine emission Spectrum of #ydrogen 6


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-ould epect that the emission and absorption spectra would much but

not the case.

The number of absorption lines is much less than the number of emission

lines.

!o absorption lines eist for hydrogen in the visible. *isible transitions

occur for transitions bac to the = level and as this is an ecited state"

electrons readily drop bac to ground state thus not absorbing phons at

this level to produce an absorption spectrum for this frequency.


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Example

Calculate the energy and frequency of the photon

than needs to be absorbed to promote an electron

from the / level to the 1 level for hydrogen.


39/54

Example

Hz

Hz h

E f

hf E

J

J

eV photonof Energy

eV E E E transition Energy

15

34

18

18

19

13

104.2

1063.6

1063.1

1063.1

106.12.10

.10

2.10

×=

×

×==

=

×=

××=

=∴

=−=∆

−

−

−


40/54

A'sorption Spectrum of the Sun(

)raunhofer lines

The core of the Sun is at a very high temperature (hundreds of millions of

I) while the outer corona has its surface layer at about 3555I.

*ery high frequencies emitted from the suns core are then absorbed by the

very hot gases closer to the sun surface and are absorbed. The line

absorption spectra can be observed on arth using a spectra scope and a

diffraction grating as a dispersion tool.

The dar absorption lines appearing in the spectrum of the Sun are called+raunhofer lines.

+rom these lines" it can be seen that sun is made up of =K1 the elements

that are here on arth.


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)luorescence

-hen an atom absorbs

high6energy photons" it is

elevated to Lecited statesM(energy states above the

ground state). cited states

are generally short6lived and

the atom quicly returns to

its ground state" often by

emitting a series of lower6energy photons. This

process of converting high6

energy photons into a larger

number of lower6energy

photons is called

LfluorescenceM


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Stimulated Emission

-hen a photon with energy corresponding to a transition from a higher6

energy state to a lower6energy state is incident on an atom in the lower

state" it can be absorbed by the atom.

0t has been discovered that when a photon with energy corresponding to a

transition from a higher6energy state to a lower6energy state is incident on

an atom in the higher state" it can stimulate a transition to the lower state.

The photon emitted in stimulated emission is identical (in energy" direction"

and phase) to the incident photon.


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Stimulated Emission

!ormally


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Stimulated Emission

-hen more atoms are simultaneously in an ecited state than in the

normal state" this is termed a population inversion"

Can be achieved by"

NOptical pumping 6 ecitation of the atoms by strong flashes (high intensity

bursts) of light whose wavelength corresponds to the transition energy of

ecitation from the ground state.

N#igh *oltage applied to a #elium !eon gas laser provides the energy to

ecite the atoms.


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Stimulated Emission

*eta Sta'le State

Some ecited states last for a relatively long time before the atomundergoes a transition to a lower6energy state by spontaneously emitting a

photon. These states are called LmetastableM states.

+or practical systems" the higher6energy state must be a metastable state

if a population inversion is to be produced.


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Application+ LASE,S

&AS4S< Light Amplification by Stimulated Emission of ,adiation

$ain components of a #eliumK!eon laser are<

N the active medium (the gas)

N a pump that supplies the energy to the tube

N components (mirrors) that enable the light to be amplified.


47/54

Application+ LASE,S

-he Active *edium

$ostly !eon gas but contains /2 #elium (vital). 0f an atom is to emit

photons by stimulation" it must have a state where an electron can residefor a relatively long period of time (meta stable state) to be stimulated by

another photon.


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Application+ LASE,S

-he Energy Supply . -he Pump

An electrical discharge consisting of a large number of electrons traverses

the tube.

These electron collide with the helium atoms and promote these atoms to

the ecited state. This occurs more readily with the #elium atoms than the

!eon atoms.


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Application+ LASE,S

Some #elium atoms collide with the !eon atoms and transfer their energy

putting !eon into an ecited state. !ormally electrons in the !eon 1 state

would dropped almost immediately to the !eon = state but because the#elium = state and the !eon 1 state are similar" ecitation to the 1 state

occurs often. This process gives rise to the population inversion.


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Application+ LASE,S

Stimulation can now occur.

-hen !eon atoms in their eited states revert to their ground state"they emit a /.?3e* photon that can stimulate the emission of the same

energy photon from nearby !eon atoms.


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Application+ LASE,S

-he -u'e . -he Amplification of the Light

The longer the emitted photons are in the tube" the more photons are

stimulated. 4eflective surfaces (mirrors) at each end of the tube providethis.

The mirrors are parallel so that light is reflected bac and forth rapidly

increasing the emissions.

One mirror is partially reflective and when the light reaches a certain

intensity" it passes through while less intense light continuos to reflect.


52/54

Application+ LASE,S

The distance between the mirrors is eactly an integral number of half

wavelengths. This allows only a certain wavelength to interfere

constructively to increase the amplitude of the wave.

2

λ n* =

The ensures that the wave is in phase as the wave amplitudes will add

in phase.

The emerging beam will have one wavelength of 31=.@nm" be

monochromatic" coherent and unidirectional.


53/54

Application+ LASE,S

/sefulness of LASE, light

N,eam does not spread out.

N,eams are intense (bright) and stay so over large distances.

N,eams are monochromatic" important in the process of reading and writing

to and from a C'.

N,eam doesnMt (almost) diverge. Can be used to align obBects over large

distances.

NStay coherent.

NCan be used as barcode scanners" weld metals" cut material" long distant

measuring devices (arth to $oon).


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Application+ LASE,S

Safe Handling of LASE,S

N#igh voltage devices" should only be opened by trained professionals.

N$ust not be shone into a persons eye.

N!ot shone onto reflective surfaces as it may reflect into someonePs eye.

N%se in a room that is well lit to ensure that the aperture of the eye is small.

1. structure of the atom (1)

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