Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

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Class 12 : Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

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1.8 Experimental Study of Photo Electric Effect :

Experiments with the photoelectric effect are performed in a discharge tube apparatus as illustrated in figure shown. The cathode of discharge tube is made up of a metal which shows photoelectric effect on which experiment is being carried out.

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

A high potential is applied to a discharge tube through a variable voltage source and a voltmeter and an ammeter are connected a measure the potential difference across the electrodes and to measure photoelectric current. Light with frequency more than threshold frequency of cathode metal is incident on it, due to which photoelectrons are emitted from the cathode. These electrons will reach the anode and constitute the photoelectric current which the ammeter will show.

Now we start the experiment by closing the switch S. Initially the variable battery source is set at zero potential. Even at zero potential variable source, ammeter will show some current because due to the initial kinetic energy some electrons will reach the anode and cause some small current will flow. But as we know majority of ejected electrons have low values of kinetic energies which are collected outside the cathode and create a could of negative charge, we call space charge, as shown in figure shown.

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

If the potential difference applied across the discharge tube is gradually increased from the variable source, positive potential of anode starts pulling electrons from the space charge. As potential difference increases, space charge decrease and simultaneously the photoelectric current in circuit also increases. This we can also see in the variation graph of current with potential difference as shown in figure shown.

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

A shown in graph, we can see as potential difference increases, current in circuit increases. But at a higher voltage VP1 space charge vanishes and at this voltage anode is able to pull the slowest electron (zero kinetic energy) ejected by the cathode. Now as all the ejected electrons from cathode start reading anode. If further potential difference is increased, it will not make any difference in the number of electrons reaching the anode hence, further increases in potential difference will not increases the current. This we can see in figure shown that beyond VP1 current in circuit becomes constant. This current is1 is called saturation current. This potential difference VP1 at which current becomes saturated is called "pinch off voltage".

Now if the frequency of incident light is kept constant and its intensity is further increased, then the number of incident photons will increase which increases the number of ejected photo electrons so current in circuit increases and now in this case at higher intensity of incident light, current will not get saturated at potential difference VP1 as now due to more electron emission, space charge will be more and it will not vanish at VP1. To pull all the electrons emitted from cathode more potential difference is required. This we can se from figure shown, that at higher intensity I2 (I2 > I1) current becomes saturated at higher value of potential difference VP2.

Intensity I2 > I1

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

Beyond VP2, we can see that all the electrons ejected from cathode are reaching the anode are current become saturated at is2 because of more electrons. Another point we can see from figure shown that when V = 0 then also current is more at high intensity incident radiation as the number of electrons of high kinetic energy are also more in the beginning which will reach anode by penetrating the space charge.

1.9. Kinetic Energies of Electrons Reaching Anode

We know that when electrons are ejected from cathode then kinetic energies may vary from 0 to Experimental Study of Photoelectric Effect Class 12 Notes | EduRev. If V is the potential difference applied across the discharge tube then it will accelerates the electron while reaching the anode. the electron which is ejected from cathode with zero kinetic energy will be the slowest one reaching the anode if its speed is v1 at anode then we have

0 + ve = Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

Similarly the electron ejected from cathode with maximum kinetic energy Experimental Study of Photoelectric Effect Class 12 Notes | EduRevwill be the fastest one when it will reach anode. If its speed is v2 at anode then we have

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

Thus we can say that all the electrons reaching anode will have their speeds distributed from v1 to v2.

1.10 Reversed Potential Across Discharge Tube :

Now the experiment is repeated with charging the polarity of source across the discharge tube. Now positive terminal of source is connected to the cathode of discharge tube. When a light beam incident on the cathode with (hv > φ ), photoelectrons are ejected and move towards anode with negative polarity.

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

Now the electrons which are ejected with very low kinetic energy are attracted back to the cathode because of its positive polarity. Those electrons which have high kinetic energies will rush toward, anode and may constitute the current in circuit.

In this case the fastest electron ejected from cathode will be retarded during its journey to anode. As the maximum kinetic energy just after emission at cathode is Experimental Study of Photoelectric Effect Class 12 Notes | EduRev, if potential difference across the discharge tube is V then the seed vf with which electrons will reach anode can be given as

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev ....(1)

Thus all the electrons which are reaching anode will have speed less then or equal to vf. Remaining electrons which have relatively low kinetic energy will either be attracted to cathode just after ejection or will return during their journey from cathode to anode. Only those electrons will case current of flow in circuit which have high kinetic energies more then eV which can overcome the electric work against electric forces on electron due to opposite polarity of source.


1.11 Cut off Potential or Stopping Potential :

We have seen with reverse polarity electrons are retarded in the discharge tube. If the potential difference is increased with reverse polarity, the number of electrons reaching anode will decrease hence photo electric current in circuit also decreases, this we can see from figure shown which shows variation of current with increase in voltage across discharge tube in opposite direction. Here we can see that at a particular reverse voltage V0, current in circuit becomes zero. This is the voltage at which the faster electron from cathode will be retarded and stopped just before reaching the anode.

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev          

Intensity I2 > I1 Frequency v (same for both radiation)

This voltage V0, we can calculate from equation (1) by substituting vf = 0 hence

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev -  eV0  = 0

or   eV0  = Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

or Experimental Study of Photoelectric Effect Class 12 Notes | EduRev ...(2)

or Experimental Study of Photoelectric Effect Class 12 Notes | EduRev ...(3)

We can see one more thing in figure shown that the graphs plotted for two different intensities I1 and I2, V0 is same. Current in both the cases in cut off at same reverse potential V0. The reason for this is equation-(2) and (3). It is clear that the value of V0 depends only on the maximum kinetic energy of the ejected electrons which depends only on frequency of light and not on intensity of light. Thus in above two graphs as frequency of incident light is same, the value of V0 is also same. This reverse potential difference V0 at which the fastest photoelectron is stopped and current in he circuit becomes zero is called cut off potential or stopping potential.

1.12 Effect of Change in Frequency of Light on Stopping Potential :

If we repeat the experiment by increasing the frequency of incident light with number of incident photons constant, the variation graph of current with voltage will be plotted as shown in figure shown. 

Frequency (v2 > v1)

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

This graph is plotted for two incident light beams of different frequency v1 and vand having same photon flux. As the number of ejected photoelectrons are same in the two cases of incident light here we can see that the pinch off voltage V01 as well as saturation current is1 are same. But as in the two cases the kinetic energy of fastest electron are different as frequencies are different, the stopping potential for the two cases will be different. In graph II as frequency of incident light is more, the maximum kinetic energy of photoelectrons will also be high and to stop it high value of stopping potential is needed. These here V01 and V02 can be given as

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev ...(4)

and Experimental Study of Photoelectric Effect Class 12 Notes | EduRev ...(5)

In general for a given metal with work function φ, if Vo is the stopping potential for an incident light of frequency v then we have

evo = hv - φ

or  evo = hv - hvth...(6)

or Experimental Study of Photoelectric Effect Class 12 Notes | EduRev ...(7)

Equation (7) shows that stopping potential V0 is linearly proportional to the frequency v of incident light. The variation of stopping potential with frequency v can be shown in figure shown. Here equation (6) can be written as

 Experimental Study of Photoelectric Effect Class 12 Notes | EduRev = evo - h(v - vth)...(8)

This equation (8) is called Einstein's Photo Electric Effect equation which gives a direction relationship between the maximum kinetic energy stopping potential frequency of incident light and the threshold frequency. 

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

Ex. 6 Find the frequency of light which ejects electrons from a metal surface fully stopped by a retarding potential of 3 V. The photo electric effect begins in this metal at frequency of Experimental Study of Photoelectric Effect Class 12 Notes | EduRev. Find the work function for this metal.

Sol. The threshold frequency for the given metal surface is

vth = 6 X1014 Hz

Thus the work function for metal surface is

φ = hvth = 6.63 X 10 -34  X 6 X1014 = 3.978 X 10-19 J

As stopping potential for the ejected electrons is 3V, the maximum kinetic energy of ejected electrons will be

KEmax = 3eV = 3 X 1.6 X10 -19 J = 4.8 X 10 -19 J

According to photo electric effect equation, we have

hv = hvth =  KEmax

or frequency of incident light is

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev= 1.32 X1015 Hz

Ex.7 Electrons with maximum kinetic energy 3eV are ejected from a metal surface by ultraviolet radiation of wavelength 1500 Å. Determine the work function of the metal, the threshold wavelength of metal and the stopping potential difference required to stop the emission of electrons.

Sol. Energy of incident photon in eV is

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

According to photo electric effect equation, we have

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

or = 8.29 - 3 eV or = 5.29 eV

Threshold wavelength for the metal surface corresponding to work function 5.29 eV is given as

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

Stopping potential for the ejected electrons can be given as

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

Ex.8 Calculate the velocity of a photo-electron, if the work function of the target material is 1.24 eV and the wavelength of incident light is 4360 Å. What retarding potential is necessary to stop the emission of the electrons ?

Sol. Energy of incident photons in eV on metal surface is

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev = 2.85 eV

According to photo electric effect equation we have

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev or Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

= 2.85 - 1.24 eV = 1.61 eV

The stopping potential for these ejected electrons can be given as

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

Ex.9 Determine the Planck's constant h if photoelectrons emitted from a surface of a certain metal by light of frequency 2.2 × 1015 Hz are fully retarded by a reverse potential of 6.6 V and those ejected by light of frequency 4.6 × 1015 Hz by a reverse potential of 16.5 eV.

Sol. From photo electric effect equation, we have

Here hv1  = φ +  2 eV01 ...(1)

and hv2  = φ +  2 eV02 ...(2)

Subtracting equation (1) from equation (2), we get

orExperimental Study of Photoelectric Effect Class 12 Notes | EduRev

or Experimental Study of Photoelectric Effect Class 12 Notes | EduRev or = 6.6 × 10-34 J-s

Ex.10 When a surface is irradiated with light of wavelength 4950 Å, a photo current appears which vanishes if a retarding potential greater than 0.6 volt is applied across the photo tube. When a different source of light is used, it is found that the critical retarding potential is changed to 1.1 volt. Find the work function of the emitting surface and the wavelength of second source. If the photo electrons (after emission from the surface) are subjected to a magnetic field of 10 tesla, what changes will be observed in the above two retarding potentials.

Sol. In first case the energy of incident photon in eV is

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev = 2.51 eV

The maximum kinetic energy of ejected electrons is

KEmax1  = eV01 = 0.6 eV

Thus work function of metal surface is given as

 φ  = E1 - KEmax1  = 2.51 - 0.6 eV = 1.91 eV

In second case the maximum kinetic energy of ejected electrons will become

KEmax2  = eV02 = 1.1 eV

Thus the incident energy of photons can be given as

E2 = φ + KEmax2 

E2 = 1.91 + 1.1 eV = 3.01 eV

Thus the wavelength of incident photons in second case will be

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

When magnetic field is present there will be no effect on the stopping potential as magnetic force can not change the kinetic energy of ejected electrons.

Ex.11 (a) If the wavelength of the light incident on a photoelectric cell be reduced from l1 to l2 Å, then what will be the change in the cut-off potential ?

(b) Light is incident on the cathode of a photocell and the stopping voltages are measured from light of two difference wavelengths. From the data given below, determine the work function of the metal of the cathode in eV and the value of the universal constant hc/e.

Wavelength (Å)                   Stopping voltage (volt)

4000                                                     1.3

4500                                                    0.9

Sol. (a) Let the work function of the surface be f. If v be the frequency of the light falling on the surface, then according to Einstein's photoelectric equation, the maximum kinetic energy KEmax of emitted electron is given by

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

We know that, KEmax = eV0

Where V0= cut-off potential.

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

Now, ΔV= V02 - V01

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev ...(1)

(b) From equation (1), we have

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev = 1.44 × 10-6 V/m

Now, Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

or Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

or φ =  2.3 eV

Ex.12 A low intensity ultraviolet light of wavelength 2271 Å irradiates a photocell made of molybdenum metal. If the stopping potential is 1.3 V, find the work function of the metal. Will the photocell work if it is irradiated by a high intensity red light of wavelength 6328 Å ?

Sol. The energy in eV of incident photons is

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev= 5.47 eV

As stopping potential for ejected electrons is 1.3 V, the maximum kinetic energy of ejected electrons will be

KEmax = eV0 = 1.3 eV

Now from photoelectric effect equation, we have

E = φ + KEmax 

or  φ = E - KEmax 

or φ = 5.47 - 1.3 eV = 4.17 eV

Energy in eV for photons for red light of wavelength 6328 Å is

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev = 1.96 eV

As E < φ, photocell will not work if irradiated by this red light no matter however intense the light will be.

2. FORCE DUE TO RADIATION (PHOTON)

Each photon has a definite energy and a definite linear momentum. All photons of light of a particular wavelength l have the same energy E = Experimental Study of Photoelectric Effect Class 12 Notes | EduRev and the same momentum p = Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

When light of intensity I falls on a surface, it exerts force on that surface. Assume absorption and reflection coefficient of surface be 'a' and 'r' and assuming no transmission.

Assume light beam falls on surface of surface area 'A' perpendicularly as shown in figure.

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

For calculating the force exerted by beam on surface, we consider following cases.

Case (I) :

a = 1, r = 0

initial momentum of the photon =Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

final momentum of photon = 0

change in momentum of photon = Experimental Study of Photoelectric Effect Class 12 Notes | EduRev (upward)

Δp =    Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

energy incident per unit time = IA

no. of photons incident per unit time =Experimental Study of Photoelectric Effect Class 12 Notes | EduRevTherefore, total change in momentum per unit time = n ΔP =Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

force on photons = total change in momentum per unit time Experimental Study of Photoelectric Effect Class 12 Notes | EduRev(upward)

Therefore, force on plate due to photon(F)   Experimental Study of Photoelectric Effect Class 12 Notes | EduRev (downward)

pressure = Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

Case : (II)

when r = 1, a = 0

initial momentum of the photon = Experimental Study of Photoelectric Effect Class 12 Notes | EduRev (downward)

final momentum of photon = Experimental Study of Photoelectric Effect Class 12 Notes | EduRev (upward)

change in momentum Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

Therefore, energy incident per unit time = I A

no. of photons incident per unit time = Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

Therefore, total change in momentum per unit time = n. DP = Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

force = total change in momentum per unit time

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev (upward on photons and downward on the plate)

pressure Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

Case : (III)

When 0 < r < 1       a + r = 1 

change in momentum of photon when it is reflected = Experimental Study of Photoelectric Effect Class 12 Notes | EduRev (upward)

change in momentum of photon when it is absorbed = Experimental Study of Photoelectric Effect Class 12 Notes | EduRev (upward)

no. of photons incident per unit time = Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

No. of photons reflected per unit time = Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

No. of photon absorbed per unit time = Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

force due to absorbed photon (FaExperimental Study of Photoelectric Effect Class 12 Notes | EduRev (downward)

Force due to reflected photon (FrExperimental Study of Photoelectric Effect Class 12 Notes | EduRev (downward)

total force = Fa + Fr

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

Now pressure P Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

Ex.13 Calculate force exerted by light beam if light is incident on surface at an angle q as shown in figure. Consider all cases.

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

Sol. Case - I

  When a = 1, r = 0

initial momentum of photon (in downward direction at an angle q with vertical) is h/λ

final momentum of photon = 0

change in momentum (in upward direction at an angle q with vertical) = Experimental Study of Photoelectric Effect Class 12 Notes | EduRev Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

energy incident per unit time = I A cos θ

Intensity = power per unit normal area

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev P = I A cos θ

No. of photons incident per unit time = Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

total change in momentum per unit time (in upward direction at an angle q with vertical)

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

Force (F) = total change in momentum per unit time

Experimental Study of Photoelectric Effect Class 12 Notes | EduRevExperimental Study of Photoelectric Effect Class 12 Notes | EduRev

Pressure = normal force per unit Area

Pressure = Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

Case II 

When r = 1, a = 0

Therefore, change in momentum of one photon

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev (upward)

No. of photons incident per unit time

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev   

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev 

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

Therefore,

∴ total change in momentum per unit time

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev =  Experimental Study of Photoelectric Effect Class 12 Notes | EduRev (upward)

Therefore,

∴ force on the plate Experimental Study of Photoelectric Effect Class 12 Notes | EduRev (downward)

Pressure Experimental Study of Photoelectric Effect Class 12 Notes | EduRev Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

Case III

when  0 < r < 1, a + r = 1

change in momentum of photon when it is reflected =Experimental Study of Photoelectric Effect Class 12 Notes | EduRev (downward)

change in momentum of photon when it is absorbed = Experimental Study of Photoelectric Effect Class 12 Notes | EduRev (in the opposite direction of incident beam)

energy incident per unit time = I A cos θ)

no. of photons incident per unit time = Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

no. of reflected photon (nr) = Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

no. of absorbed photon (nQ) = Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

force on plate due to absorbed photons Fa = na. ΔPa

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev (at an angle θ with vertical Experimental Study of Photoelectric Effect Class 12 Notes | EduRev)

force on plate due to reflected photons Fr = nr ΔPr

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev (vertically downward)

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

now resultant force is given by   = Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

and, pressure Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

Ex.14 A perfectly reflecting solid sphere of radius r is kept in the path of a parallel beam of light of large aperture. If the beam carries an intensity I, find the force exerted by the beam on the sphere.

Sol. Let O be the centre of the sphere and OZ be the line opposite to the incident beam (figure). Consider a radius about OZ to get a making an angle q with OZ. Rotate this radius about OZ to get a circle on the sphere. Change q to q +dq and rotate the radius about OZ to get another circle on the sphere. The part of the sphere between these circles is a ring of area 2pr2 sinq dq. Consider a small part DA of this ring at P. Energy of light falling on this part in time Dt is

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

ΔU = IΔt(ΔA cos θ) 

The momentum of this light falling on ΔA is ΔU/c along QP. The light is reflected by the sphere along PR. The change in momentum is

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev (direction along Experimental Study of Photoelectric Effect Class 12 Notes | EduRev)

The force on ΔA due to the light falling on it, is

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev (direction along Experimental Study of Photoelectric Effect Class 12 Notes | EduRev)

The resultant force on the ring as well as on the sphere is along ZO by symmetry. The component of the force on DA along ZO

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

The force acting on the ring is  dF = Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

The force on the entire sphere is Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

Experimental Study of Photoelectric Effect Class 12 Notes | EduRevExperimental Study of Photoelectric Effect Class 12 Notes | EduRev

Note that integration is done only for the hemisphere that faces the incident beam.

3. De-broglie wavelength of matter wave

A photon of frequency v and wavelength λ has energy.

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

By Einstein's energy mass relation, E = mc2 the equivalent mass m of the photon is given by.

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev . ..(i)

or Experimental Study of Photoelectric Effect Class 12 Notes | EduRev or Experimental Study of Photoelectric Effect Class 12 Notes | EduRev...(ii)

Here p is the momentum of photon. By analogy de-Broglie suggested that a particle of mass m moving with speed v behaves in some ways like waves of wavelength λ (called de-Broglie wavelength and the wave is called matter wave) given by,

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev...(iii)

where p is the momentum of the particle. Momentum is related to the kinetic energy by the equation,

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

and a charge q when accelerated by a potential difference V gains a kinetic energy K = qV. Combining all these relations Eq. (iii), can be written as,

 Experimental Study of Photoelectric Effect Class 12 Notes | EduRev (de=Broglie wavelength)....(iv)

3.1 de-Broglie wavelength for an electron

If an electron (charge = e) is accelerated by a potential of V volts, it acquires a kinetic energy,

K = eV

Substituting the value of h, m and q in Eq. (iv), we get a simple formula for calculating de-Broglie wavelength of an electron.

Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

3.2 de-Broglie wavelength of a gas molecule :

let us consider a gas molecule at absolute temperature T. Kinetic energy of gas molecule is given by

K.E. = Experimental Study of Photoelectric Effect Class 12 Notes | EduRev kT ; k = Boltzman constant

λgas molecules =Experimental Study of Photoelectric Effect Class 12 Notes | EduRev

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