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## Dual Nature Of Radiation And Matter

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De-Broglie wavelength of particle passing through a potential
The De-Broglie wavelength is the wavelength , associated with a object and is related to its momentum and mass.
The De-Broglie relation for a particle is given by,

or
where, is wavelength
h is plank's constant
p is momentum
m is mass
v is speed
Consider an electron (mass m, charge e) accelerated from rest through a potential V. The kinetic energy K of the electron equals the work done (eV ) on it by the electric field: K = eV
Now,
so that,

The De-Broglie wavelength is given by,

Substituting the numerical values of h, m, e, we get
nm
where V is the magnitude of accelerating potential in volts.
For a 120 V accelerating potential, nm.
A - particle is accelerated through a potential difference of V volts from rest. The de-Broglie wavelength associated with it is (in angstrom):
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B
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Dual nature of matter was proposed by de Broglie in 1923, it was experimentally verified by Davisson and Germer by diffraction experiment. Wave character of matter has significance only for microscopic particles. de Broglie wavelength or wavelength of matter wave can be calculated using the following relation: where, '' and '' are the mass and velocity of the particle. de Broglie hypothesis suggested that electron waves were being diffracted by the target, much as -rays are diffracted by planes of atoms in the crystals.
An electron microscope is used to probe the atomic arrangements to a resolution of . What should be the electric potential to which the electrons need to be accelerated?
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de Broglie Wavelength
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## Failure of the wave theory of light failing to explain the photoelectric effect

According to Wave Theory, light is an electromagnetic wave consisting of electric and magnetic fields with a continuous distribution of energy over the region over which the wave extends. This wave picture of light could not explain the basic features of light as explained below : According to the Wave Theory when a wavefront of light strikes a metal surface, the free electrons at the surface absorb the radiant energy continuously. The greater the intensity of incident radiation, the greater are the amplitudes of electric and magnetic fields and the greater is the energy density of the wave. Hence higher intensity should liberate photoelectrons with greater kinetic energy. But this is contrary to the experimental result that the maximum kinetic energy of the photoelectrons does not depend upon the intensity of incident radiation. No matter what the frequency of incident radiation is, a light wave of sufficient intensity (over a sufficient time) should be able to impart enough energy required to eject the electrons from the metal surface. Thus the Wave Theory fails to explain the existence of threshold frequency. The energy of the light waves is smoothly and evenly distributed across their advancing wavefront. Each electron intercepts an insignificantly small amount of this energy and so it should require a finite time to escape from the metal surface. But actually, the emission is almost instantaneous.

## How to find Planck's constant experimentally

In this experiment, you will use light-emitting diodes (LEDs) to measure Planck's constant.
##### Procedure
The circuit that will be used to experimentally determine Planck's constant is illustrated below.  The A input to the 750 interface measures the voltage across the 1000 W resistor in series with the LED. This voltage is directly proportional to the current through the LED, and its value is numerically equal to the current in mA. The B input reads the total voltage across the LED and the 1000 W series resistor. The difference between these two voltages is the voltage across the LED. To perform the experiment, the voltage probes are connected to the first two analog inputs of the 750 interface and the Pasco Data Studio program is used to record the voltages as the potentiometer is turned from its minimum (fully counterclockwise) to its maximum (fully clockwise) position. In this way, thousands of data points may be acquired in a few seconds. After the data is collected, it is scanned to determine the least value at which the resistor voltage becomes nonzero. This is the turn on voltage, Vo, for that particular LED. By using different LED's of different color (different maximum wavelength, ) and by measuring the corresponding value of Vo, a table of data of Vo versus can be developed. A graph of Vo versus 1/λ is plotted which has a slope of hc/e, from which h is determined. A typical graph of Vo versus for several LED's is shown below.  3
Characteristics of photons:
According to particle nature of light, photons are the basic constituents of any radiation and possess the following characteristic properties:
(i) The photons of light of frequency and wavelength will have energy, given by
(ii) The energy of a photon is determined by the frequency of the radiation and not by its intensity and the intensity has no relation with the energy of the individual photons in the beam.
(iii) The photons travel with the velocity of light and its momentum is given by p
(iv) Since photons are electrically neutral, they are unaffected by electric and magnetic fields.
(v) When a photon interacts with matter (photon-electron collision), the total energy, total linear momentum and angular momentum are conserved. Since photon may be absorbed or a new photon may be produced in such interactions, the number of photons may not be conserve.  