dual nature of matter 1

8/8/2019 Dual Nature of Matter 1

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Work function ( 0)

Metals have free electrons (valenceelectrons ). To be freed from the metal,

they need someminimum energy, called work function ofthe metal. The work function of a metaldepends upon the type of the metal andits temperature.

It is generally denoted by 0

d d i V ( l t lt)


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(i) Thermionic emission(ii) Field emission(iii) Photo-electric emission(iv) secondary emission


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Work functionA certain minimum amount of energy is

required to be given to an electron to pullit out from the surface of the metal. Thisminimum energy required by an electronto escape from the metal surface is called

the work function of the metal.

Note from Table 11.1 that the work function of

l ti i th hi h t (5 65 V) hil it i th


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Electron emission

The minimum energy required for the electron

emission from the metal surface can be suppliedto the free electrons by any one of the followingphysical processes:

(i) Thermionic emission: By suitably heating,sufficient thermal energy can be imparted to thefree electrons to enable them to come out of themetal. Such emission occurs in diode, triode and

TV t b ( C th d t b )


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(iv) secondary emission: it occurs when fast

moving electrons ( high energy electrons,called primary electrons) strike the metalsurface. They transfer their energy to the freeelectrons of the metal. The so emittedelectrons are called secondary electrons.


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Effect of intensity of light on

photocurrent

Keeping the frequency of the incidentradiation and the accelerating potential fixed


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per second. This implies that the numberof photoelectrons emitted per second isdirectly proportional to the intensity ofincident radiation.

Effect of potential on photoelectriccurrent


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These observations have two implications:

(i) The maximum kinetic energy of thephotoelectrons varies linearly with thefrequency of incident radiation, but isindependent of its intensity.

(ii) For a frequencyv of incident radiation,lower than the cut-off frequency v0, nophotoelectric emission is possible even ifthe intensity is large.


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Laws of photoelectric effect

(i) For a given photosensitive material andfrequency of incident radiation (above thethreshold frequency), the photoelectriccurrent is directly proportional to the

intensity of incident light (Fig. 11.2).


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its intensity (Fig. 11.3).

(iii) For a given photosensitive material,there exists a certain minimum cut-off


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(iv) The photoelectric emission is aninstantaneous process without anyapparent time lag (10-9 s or less), evenwhen the incident radiation is made


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Wave theory fails to explain the characteristics of

photoelectric effect.

( 1 ) According to the wave theory, energy and intensity oflight wave depend on its amplitude. Hence energy of photo-

electrons should increase with intensity of light. But

experimental results indicate that the energy of photo-

electrons does not depend uponthe intensity of light.

( 2 ) According to the wave theory, energy of light has no


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high frequency, emission of photo-electrons is immediate

even if its intensity is low.


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The intensity of electron beam scattered at different angles

of scattering can be measured for the given accelerating

voltage.

Angle of scattering ( ) is the angle between the incidentbeam and scattered beam of electrons. The graph in polarcoordinates of intensity for the observations taken byDavisson and Germer between 44 V and 68 V are shown

qualitatively in the figure given below.

The graphs indicate angle at which maximum scattering

occurs for a given voltage. It is 50 for 54 V.


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Heisenbergs uncertainty principle

If the uncertainty in the x-coordinate of the position of a

particle is x and uncertainty in the x-component ofits momentum is p, then

x . p h / 2

x 0 p

and p 0 x


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Einsteins photoelectric equation

Einstein described the photoelectric effectas a consequence of conservation of energy

as

hv = W0 + (KE)max

Here vis the frequency of incident radiationAnd W0 is called work function.

The value of work function is constant for a


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Work Function It is the minimum amount of energy

required to eject an electron from thesurface of the metal.

It is related to the threshold frequency v0asW0 = hv0

It follows that when v=v0 the kineticenergy of photoelectrons will be zero.

Work function is inversely proportional to


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It depends on the frequency of incident

light ashv = W0 + (KE)maxor(KE)max= hv - W0i.e (KE)max hv

It does not depend upon intensity ofincident radiation.

Number of photoelectrons emitted

Depends upon the intensity of incidentlight Independent of the frequency of the

incident light, provided v >v0


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The Photoelectric Effect

The remarkable aspects ofthe photoelectric effect

when it was first observedwere:

1. The electrons wereemitted immediately -no time lag!

2. Increasing theintensity of the lightincreased the numberof photoelectrons, but


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suggested a particle nature for light. Then electrons too

were found to exhibit dual natures.


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DeBroglie Hypothesis

Starting with the Einstein formula:

Another way of expressing this is

Therefore, for a particle ofzero rest mass


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Failures of Classical Physics

Some experimental situations where "classical"physics fails:

Photoelectric

effect Blackbody radiation

Line spectraPhysiological effects of

radiation

Wave properties of electron (electronmicroscope)

Davisson-Germer Experiment


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Davisson-Germer Experiment


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DeBroglie Wavelengths

The Davisson-Germer

experiment showed that

electrons exhibit the

DeBroglie wavelength given

by:


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DeBroglie


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DeBroglieWavelengths


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Photon Energies for EM Spectrum


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Photon Energies for EM Spectrum

The Electromagnetic Spectrum


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The Electromagnetic Spectrum


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Spectral Colors


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Spectral Colors

Examples of Electron Waves


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Wave Nature of Electron


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Wave Nature of Electron


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dual nature of matter 1

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