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FAILURE OF WAVE THEORY/CLASSICAL PHYSICS TO EXPLAIN PHOTOELECTRIC EFFECT
The wave theory of radiation failed to explain photoelectric effect. This will become clear from the following discussion.
I. According to wave theory of radiation the greater the intensity of the wave the greater the energy of the wave.
So wave theory does explain why the number of emitted photoelectrons increase as the intensity of radiation is increased.
But it fails to explain the experimentally observed fact that the velocity or kinetic energy of the emitted photoelectron is independent of the intensity of incident radiation.
According to the wave theory, an increasing in the intensity of radiation should increase the kinetic energy of the emitted photoelectrons but it is contrary to the experimentally observed fact.
II. According to wave theory, intensity of radiation is independent of it is frequency it depends upon the amplitude of electric field vector.
Therefore, an increase in the frequency of radiation should not affect the velocity or kinetic energy of the emitted electrons.
But it is observed experimentally that if the frequency of the incident radiation is increased, the kinetic energy of the emitted electrons also increases.

III. According to the wave theory, electrons should always be emitted from a metal by radiation of any frequency if the incident been is strong enough.
However experiments show that no matter how great is the intensity of the incident radiation; no electrons are emitted from the metallic surface if the frequency of radiation is less than a particular value i.e. threshold frequency.

IV. According to the wave theory the energy of radiation is spread continuously over the wave fronts of the radiation.
Therefore, a single electron in the metal will intercept only a small fraction of the wave’s energy.
Consequently considerable time should be needed for an electron to absorb enough energy from the wave to escape the metal surface.
But experiment show that electron are emitted as soon as radiation of suitable frequency falls on the metallic surface.
In other words photoelectric emission is instantaneous there is no delay.
The above discussion is a convincing proof of the inability of the wave theory to explain the photoelectric effect.
EINSTEIN QUANTUM THEORY OF LIGHT
Einstein explained photoelectric effect on the basis of Planck’s quantum theory.
According to Einstein light radiation consist of tiny packets of energy called quanta.
Photon
Photon is the single quantum of light radiation which travels with the speed of light.
The energy of a photon is given by E.

E=hf
where
f –frequency of light radiation
h – Plank’s constant.
Further, Einstein assumed that one photon of suitable frequency (=fo or >fo) can eject only one photoelectron from the metal surface.
He suggested that the energy of a single photon cannot be shared among the free electron in the metal.
Only one electron can absorb the energy of a single photon.
EINSTEIN’S PHOTOELECTRIC EQUATION
According to Einstein, one photoelectron is emitted from a metal surface if one photon of suitable frequency is incident on the metal.
Suppose a photon of suitable frequency f (< than the fo for the metal) is incident on the metal.
EcoleBooks | PHYSICS A LEVEL(FORM SIX) NOTES - PLANCK’S QUANTUM THEORY OF BLACK BODY RADIATION(3)
The energy hf of the photon is spent in two ways
I. A part of photon energy is used in liberating the least tight bound electron from the metal surface which is equal to the work functio
n W0 of the metal.
II. The rest of the energy of photon appears as maximum kinetic energy of the emitted electron.
Einstein summarized this idea in what is called the Einstein photoelectric equation.
Photon = work function + maximum kinetic energy


EcoleBooks | PHYSICS A LEVEL(FORM SIX) NOTES - PLANCK’S QUANTUM THEORY OF BLACK BODY RADIATION(3)
The above equation is known as Einstein’s photoelectric equation

EcoleBooks | PHYSICS A LEVEL(FORM SIX) NOTES - PLANCK’S QUANTUM THEORY OF BLACK BODY RADIATION(3)
If the frequency of the incident radiation is fo then the emitted photoelectron will have zero velocity.
EcoleBooks | PHYSICS A LEVEL(FORM SIX) NOTES - PLANCK’S QUANTUM THEORY OF BLACK BODY RADIATION(3)
Maximum kinetic Energy of emitted photoelectrons is
EcoleBooks | PHYSICS A LEVEL(FORM SIX) NOTES - PLANCK’S QUANTUM THEORY OF BLACK BODY RADIATION(3)
If f < fo, then from above equation K.Emax is negative which is impossible therefore, photoelectrons emission cannot occur if the frequency of incident radiation is less than fo.
If f > fo, then equation above K.Emax α f. This means that max kinetic energy of photoelectrons depends only on the frequency (f) of the incident radiation.


NUCLEAR PHYSICS
RADIOACTIVITY
This is the em
ission of radiations from heavily elements such as uranium whose nuclei are unstable.
Radiations emitted are called alpha EcoleBooks | PHYSICS A LEVEL(FORM SIX) NOTES - PLANCK’S QUANTUM THEORY OF BLACK BODY RADIATION(3) , Beta (β) particles and gamma EcoleBooks | PHYSICS A LEVEL(FORM SIX) NOTES - PLANCK’S QUANTUM THEORY OF BLACK BODY RADIATION(3)rays.
RATE OF DISINTEGRATION
The number of atoms of radioactive elements disintegrating per second EcoleBooks | PHYSICS A LEVEL(FORM SIX) NOTES - PLANCK’S QUANTUM THEORY OF BLACK BODY RADIATION(3) is directly proportional to the number of atom present at that instant.
EcoleBooks | PHYSICS A LEVEL(FORM SIX) NOTES - PLANCK’S QUANTUM THEORY OF BLACK BODY RADIATION(3)
Where λ = decay constant
The negative sign (-) indicates that N decreases as time (t) increases.
If N0 is the number of atoms at time t= 0 and N is the number of atoms at time t. then:-
EcoleBooks | PHYSICS A LEVEL(FORM SIX) NOTES - PLANCK’S QUANTUM THEORY OF BLACK BODY RADIATION(3)
HALF LIFE
The half life time EcoleBooks | PHYSICS A LEVEL(FORM SIX) NOTES - PLANCK’S QUANTUM THEORY OF BLACK BODY RADIATION(3)of a radioactive element is the times taken for the atoms disintegrate to half their initial number.
NECTA 1994/1/19
Draw a graph of EcoleBooks | PHYSICS A LEVEL(FORM SIX) NOTES - PLANCK’S QUANTUM THEORY OF BLACK BODY RADIATION(3)
SOLUTION:
This is the graph of radioactive decay in time.
EcoleBooks | PHYSICS A LEVEL(FORM SIX) NOTES - PLANCK’S QUANTUM THEORY OF BLACK BODY RADIATION(3)
EcoleBooks | PHYSICS A LEVEL(FORM SIX) NOTES - PLANCK’S QUANTUM THEORY OF BLACK BODY RADIATION(3)




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EcoleBooks | PHYSICS A LEVEL(FORM SIX) NOTES - PLANCK’S QUANTUM THEORY OF BLACK BODY RADIATION(3)

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