Dual Nature Notes -2014

DELHI PRIVATE SCHOOL,SHARJAH Unit- Dual Nature of Matter and Radiation Electron Emission and Photoelectric Effect The phenomenon of emission of electrons from the surface of a metal is called electron emission.

Work function − A certain minimum amount of energy is required to be given to an electron to pull it out from the surface of the metal. This minimum energy required by an electron to escape from the metal surface is called the work function of the metal. The minimum energy required for the electron emission from the metal surface can be supplied to the free electrons by any one of the following physical processes:

Work Functions for Photoelectric Effect Element Cesium Sodium Potassium Calcium Uranium Magnesium Cadmium Aluminum Lead Niobium

Work Function(eV) 2.1 2.28 2.3 2.9 3.6 3.68 4.07 4.08 4.14 4.3

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Zinc Iron Mercury Copper Silver Carbon Beryllium Cobalt Nickel Gold Selenium Platinum

4.3 4.5 4.5 4.7 4.73 4.81 5 5 5.01 5.1 5.11 6.35

Thermionic emission − By suitable heating, sufficient thermal energy can be imparted to the free electrons to enable them to come out of the metal. Field emission − By applying a very strong electric field to a metal, electrons can be pulled out of the metal. Photoelectric emission: is the phenomenon of ejection of electrons from a metal surface when light of suitable frequency is incident on it. The electrons emitted are called photoelectrons and the current produced in the circuit is called photoelectric current .

Experimental setup to explain photoelectric emission [Lenard’s observations]:- Lenard observed that when ultraviolet radiations were allowed to fall on the emitter plate P of an evacuated tube enclosing two electrodes (metal plates), current flows in the circuit. As soon as the ultraviolet radiations were stopped, the current flow also stopped.

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The apparatus consists of an evacuated glass or quartz tube, which encloses a photosensitive plate C and a metal plate A. The window W will allow the light of a particular frequency to pass through it.When a monochromatic radiation of suitable frequency obtained from source S falls on the photosensitive plate C, the photoelectrons are emitted from C, which get accelerated towards the plate A (kept at positive potential). These electrons flow in the outer circuit, resulting in the photoelectric current. Due to this, the microammeter shows a deflection. Factors affecting photoelectric current: a) Effect of intensity of incident radiation on photoelectric current By keeping frequency of incident radiation constant and plate A at a positive potential, when the intensity of incident radiation increases, number of photoelectrons emitted also increases . The number of photoelectrons emitted per second is directly proportional to the intensity ofincident radiation.

b)Effect of potential on photoelectric current

Keep plate A at some positive accelerating potential with respect to plate C and illuminate plate C with light of fixed frequency ν and fixed intensity I1.

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It is found that photoelectric current increases with increase in accelerating potential. At some stage, for a certain positive potential of plate A, all the emitted electrons are collected by plate A and the photoelectric current becomes maximum or saturates. This maximum value of photoelectric current is called saturation current.

When intensity of light is increased, I2>I1 and frequency kept constant, the saturation current is greater, but the stopping potential remains the same. Stopping potential The minimum negative potential V0 given to plate A with respect to plate C at which the photoelectric current becomes zero is called stopping potential or cut off potential. If e is the charge on the photoelectron, then ...Work done by the stopping potential = Maximum KE of electrons i.e. eV0 = ½ mVmax2 = KEmax As charge of as electron is constant V0 is a measure of maximum KE of photoelectrons c)Effect of frequency of the incident radiation Taking radiations of different frequencies but of same intensity, the variation between photoelectric current and potential of plate A is obtained and shown in graph given below.

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From the graph, we note that (i) The value of stopping potential is different for radiation of different frequency. (ii) The value of stopping potential is more negative for radiation of higher incident frequency. (iii) The value of saturation current depends on the intensity of incident radiation, but is independent of the frequency of the incident radiation. Graph between stopping potential and the frequency of the incident radiation:

From the graph, we note: 1) 2)

Stopping potential is proportional to frequency. At ν0, stopping potential if zero and photoelectric current is zero.

Threshold frequency ν0 is the minimum cut-off frequency of incident radiation for a given metal surface below which no photoelectrons are emitted.(stopping potential is zero) Current with frequency at constant intensity

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Photoelectric current

V0

frequency

Maximum KE is independent of incident light (graph a) and depends only upon its frequency (graph b).

ν0 frequency graph b

Laws of Photoelectric emission 1.

For a given metal surface and frequency of incident radiation, photoelectric current is directly proportional to the intensity of incident light. 2. For a given metal, there exits a curtain minimum frequency of incident radiation below which no photoelectrons are emitted. This frequency is called threshold frequency.

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3.

Above the threshold frequency, maximum KE of photoelectrons emitted is independent of the intensity of incident light, but depends only upon the frequency of incident light. 4. Photoelectric emission is instantaneous. Particle nature of light Photon theory of radiations According to Max Planck, radiations are emitted as packets of energy called photons. The energy of each photon is directly proportional to the frequency of radiations. i.e. E α v

or E = h v

Photons: are packets of energy emitted by a source of electromagnetic radiation.

Properties of photons: 1.

They travel in straight lines with the speed of light.

2.

Energy of each photon: E = h ν = h c/λ Where h = 6.62 x 10-34 Js

3.

Photon has zero rest mass m = m0/(1 – v2/C2)1/2 When velocity of photon v=c, m0 = 0. i.e photon cannot exist in rest. m = E/c2 = hν/c2

4.

A Photon of energy E possesses mass

5.

Momentum of each photon = mc = E/c = hν/c=h/λ

6.

All photons of light have the same frequency, energy and momentum, independent of the intensity of radiation. By increasing the intensity of light of given wavelength, there is only an increase in the number of photons per second crossing a given area, with each photon having the same energy.

7.

Photons are electrically neutral and are not deflected by electric and magnetic fields.

8.

In a photon particle collision, the total energy and total momentum are conserved. However, the number of photons may not be conserved in a collision. The photon may be absorbed or a new photon may be created.

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Einstein’s Photoelectric Equation When a photon of light of frequency ν is incident on a photosensitive metal surface, the energy of the incident photon hν is spent in a) overcoming the surface barrier equal to the work function Φ0 of the metal and b) the rest in imparting KE to the emitted photoelectrons hν = Φ0 + ½ mv2 …(1) Work function Φ0 or threshold energy is the minimum energy that must be supplied to the electron so that it ejects from the metal surface. Φ0 = h ν0 where ν0 is the threshold frequency Therefore (1) becomes hν = h ν0 + ½ mvmax2 ½ mvmax2 = hν – hν0 Verification of photoelectric emission 1. a) KE cannot be negative implies that hν = hν0 + ½ mvmax2 . . . hν > hν0 photoelectric emission takes place if ν > ν0 if ν < ν0 , no photoelectric emission takes place. 2. One photon can emit only one electron from the metal surface, so the number of photoelectrons emitted per second is directly proportional to the intensity of incident light which depends upon number of protons present in the incident light. 3. It is clear that kinetic energy, 1/2mv2 α frequency, v because Planck’s constant, h and cut off frequency, v0 are constant for a given photo emitter. This shows that K.E. of photoelectron is directly proportional to the frequency of the in the incident light. 4. Photoelectric emission is due to elastic collision between a photon and an electron in the substance. As such there can not be any significant time lag between incidence of photons and emission of photoelectron. Thus, the process of electric emission instantantaneous.

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Significance of V0 – ν graph. To find the value of h

According to Einstein’s photoelectric equation. hν = hν0 + ½ mvmax2 ½ mvmax2 = hν - hν0 eV0 = hν - hν0 V0 = (h/e) ν – (h/eν0)

(1)

(2)

Equation (2) is of the form y = mx + c (3) comparing (2) and (3) slope of V0 – ν graph. = h/e . . . Value of h = e x slope The value of h calculated from the graph if in agreement with the theoretical value. Millikan performed experiment on photoelectric effect and plotted graph between different stopping potentials and the corresponding frequencies as given beside. The value of ‘h’ determined from the graph using the equation (1) is found to be the same as its theoretical value. This verifies the Einstein’s photoelectric equation.

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Photocell – is an arrangement which converts light into electrical energy.

Construction It consists of a thin glass enclosed in a highly evacuated glass bulb. The cathode C is a parabolic metal surface made of photosensitive metal such as Cesium and anode A series as a collector of photoelectrons. Uses: - In an automatic controlling of street light, reproduction of audio in motion pictures, burglar alarms for detecting minor flaws or holes in metal sheets etc. Working When light of frequency ν > ν0 falls of the cathode, photoelectrons are emitted. These electrons are attracted to the anode and measured.

de-Broglie hypothesis According to de – Broglie, a wave is associated with every moving particle. These waves are called de-Broglie waves or matter waves. Wave nature of matter de-Broglie relation) Nature itself exists in two forms matter and radiation. Radiation possesses dual nature. Hence de- Broglie argued that matter also should possess dual nature. i.e. particle and wave. Further, he determined the wavelength associated with a particle of mass ‘m’ moving with a velocity ‘v’, using Einstein’s mass-energy relation and Planck’s quantum theory as follows: According to quantum theory of radiation, energy of a photon of frequency ν, E =hv [Planck’s relation]. –(1)

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If ‘m’ is the mass of the photon considered as a particle, according to Einstein’s mass energy relation E = mc2 =pc ----(2) [Einstein’s relation] From (1) and (2) pc = hν p = hν/c = h/λ de-Broglie wavelength λ = h/p This relation connects momentum which is characteristic of the particle and wavelength which is characteristic of the wave. If ‘m’ is the mass of the particle moving with velocity ‘v’ λ = h/mv Conclusions : 1. Lighter the particle, greater is the de Broglie wavelength . 2. Faster the particle, smaller is the de Broglie wavelength. 3. de Broglie wavelength is independent of nature or charge of the particle. 4. Matter waves are not electromagnetic in nature. de-Broglie wavelength of electron Consider an electron of mass ‘m’ and charge ‘e’ accelerated through a potential difference V. If E is the energy acquired by the particle E = eV -(1) If ‘v’ is the velocity of the particle, E = ½ mv2 -(2) From (1) and (2) ½ mv2 = eV v = √2E/m ∴de-Broglie wavelength of electron, λ = h/mv = λ = h/√2mE or λ = h/√2meV Knowing m, e of electron, λ = 12.27/√V Å Davisson and Germer experiment To demonstrate wave nature of electrons. It is the first experimental set up to establish the wave nature of matter and hence to verify de-Broglie’s relation. It based on the principle of diffraction of electron when scattered by crystals. The experiment arrangement as shown below:

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A beam of electrons from hot tungsten cathode accelerated by a potential difference V is made to strike the nickel crystal. The electrons are scattered in all directions by the atoms in the crystal. The intensity of scattered beam for different values of angles of scattering θ is detected by the moving detector and measured. The experiment is repeated using different accelerating voltages, from 44V to 68V.. From the graph between intensity of scattered beam of electrons at different angles of scattering and at different accelerated voltages, it was found that maximum intensity of scattered beam was at a potential difference of 54V. The appearance of the peak in the graph is due to the constructive interference of electrons scattered from the different layers of the crystal. According to Bragg’s law for 1st order diffraction maximum 2d sinθ = nλ n = 1,Φ = 65 0,θ = 50 0,d = 0.91Å ,λ = 1.66Å de-Broglie wavelength of electron at V = 54V is λ=12.27/√V = 1.65Å ∴ The two results were in close agreement between the theoretical value and the experiment value. hence the experiment could establish the existence of matter waves and wave nature of electron. Note: - The wave properties of electrons have been utilized in the design of electron microscope which is a great improvement, with higher resolution, over the optical microscope.

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