Advertisements
Advertisements
प्रश्न
State Einstein’s photoelectric equation. Explain all characteristics of the photoelectric effect, on the basis of Einstein’s photoelectric equation.
Advertisements
उत्तर
Einstein’s photoelectric equation: K.E.max = (hν – `phi_0`)
Characteristics of photoelectric effect:
- The photoelectric work function `phi_0` is constant for a given emitter. Hence if the frequency ‘ν’ of the incident radiation is decreased, the maximum kinetic energy of the emitted photoelectrons decreases, till it becomes zero for a certain frequency ν0. Therefore, from Einstein’s equation,
0 = hv0 - `phi_0`
∴ `phi_0` = hv0 .......….(1)
This shows that the threshold frequency is related to the work function of the metal and hence it has different values for different metals. - Using equation (1), Einstein’s equation can be written as
`1/2"mv"_"max"^2 = "hv" - "hv"_0`
∴ `1/2"mv"_"max"^2 = "h"("v" - "v"_0)`
This equation shows that:
a. If ν < ν0, then K.E is negative, which is not possible. In this case, photoelectric emission is not possible.
b. If ν > ν0, then photoelectrons move with some velocity.
∴ K.E > 0, which is possible. Hence, photoelectrons are emitted.
c. If ν = ν0, the photoelectrons are just emitted. In this case, K.E = 0. - The photoelectric equation is,
`1/2"mv"_"max"^2 = "hv" - phi_0` .....….(2)
where, hν = energy of the photon of incident radiation.
`phi_0 = "hv"_0` = photoelectric work function of the metal.
Thus, both the terms on the R.H.S of equation (2) depends on the frequency and not on the intensity of radiation. Hence the maximum kinetic energy with which photoelectrons are emitted is independent of the intensity of radiation. However, since `phi_0` and h are constants, the maximum kinetic energy of the photoelectrons is directly proportional to the frequency. - According to the quantum theory, when the intensity of the radiation increases, there is a proportional increase in the number of photons incident per second on the surface. One photon can cause the emission of one photoelectron. Therefore, with the increase in the intensity of radiation, there will be an increase in the photoelectron interactions and the rate of emission of electrons.
- The emission of a photoelectron is the result of a collision between a photon and an electron. As soon as the radiation is incident on the photosensitive surface, the entire energy of the photon is absorbed by the electron at once. Therefore, the electrons are emitted at a moment when light is incident on the metal surface. This explains why photoelectric emission is instantaneous.
- If the electron, with which the incident photon collides, is situated on the emitting surface, the electron will be ejected with maximum K.E as given by Einstein’s equation.
- If, however, the electron is situated in the interior of the emitting material, it will lose some energy in coming to the surface. This explains why the photoelectrons are emitted with different kinetic energies.
Thus, all the features of the photoelectric effect are explained.
APPEARS IN
संबंधित प्रश्न
If the frequency of incident light falling on a photosensitive material is doubled, then the kinetic energy of the emitted photoelectron will be ______.
Is it always possible to see the photoelectric effect with a red light?
It is observed in an experiment on the photoelectric effect that an increase in the intensity of the incident radiation does not change the maximum kinetic energy of the electrons. Where does the extra energy of the incident radiation go? Is it lost? State your answer with explanatory reasoning.
Given the following data for incident wavelength and the stopping potential obtained from an experiment on the photoelectric effect, estimate the value of Planck's constant and the work function of the cathode material. What is the threshold frequency and corresponding wavelength? What is the most likely metal used for emitter?
| Incident wavelength (in Å) | 2536 | 3650 |
| Stopping potential (in V) |
1.95 | 0.5 |
The electrons are emitted in the photoelectric effect from a metal surface.
As the intensity of incident light increases ______
With the help of a circuit diagram describing an experiment to study the photoelectric effect.
The maximum velocity of the photoelectron emitted by the metal surface is v. Charge and the mass of the photoelectron is denoted by e and m, respectively. The stopping potential in volt is ______.
The graph of stopping potential `"V"_"s"` against frequency v of incident radiation is plotted for two different metals P and Q as shown in the graph. ΦP and ΦQ are work-functions of P and Q respectively, then
If the maximum kinetic energy of emitted electrons in photoelectric effect is 3.2 × 10-19 J and the work-function for metal is 6.63 × 10-19 J, then stopping potential and threshold wavelength respectively are
[Planck's constant, h = 6.63 × 1034 J-s]
[Velocity of light, c = 3 × 108 `"m"/"s"`]
[Charge on electron= 1.6 × 10-19 C]
Which one of the following statements ts INCORRECT for stopping potential in photoelectric emission?
When a certain metallic surface is illuminated with monochromatic light of wavelength '`lambda`', the stopping potential for photoelectric effect is '3V0'. If the same surface is illuminated with a light of wavelength '`2 lambda`', the stopping potential is found as 'V0'. The threshold wavelength for this surface is ____________.
An electromagnetic wave of wavelength '`lambda`' is incident on a photosensitive surface of negligible work function. If the photoelectrons emitted from this surface have the de-Broglie wavelength '`lambda_1`' then ____________.
The ratio of slopes m1: ro2 of the lines given in the following graphs is, ______.
In experiment of photoelectric effect, the stopping potential for incident yellow light of wavelength 5890 Å is 4 volt. If the yellow light is replaced by blue light of wavelength 4000 Å, the stopping potential is ____________.
The radiation corresponding to the 3 → 2 transition of a hydrogen atom falls on a gold surface to generate photoelectrons. These electrons are passed through a magnetic field of 5 × 10-4 T. Assume that the radius of the largest circular path followed by these electrons is 7 mm, and the work function of the metal is ______.
(Mass of electron = 9.1 × 10-31 kg)
In a photoelectric experiment, ultraviolet light of wavelength 280 nm is used with a lithium cathode having work function Φ = 2.5 eV. If the wavelength of incident light is switched to 400 nm, find out the change in the stopping potential.
(h = 6.63 × 10-34 Js, c = 3 × 108 ms-1)
When radiation of wavelength λ is used to illuminate a metallic surface, the stopping potential is V. When the same surface is illuminated with radiation of wavelength 3λ, the stopping potential is `"V"/4`. If the threshold wavelength for the metallic surface is nλ. then value of n will be ______.
Photoelectrons are observed to just emit out of a material surface when the light of 620 nm falls on it with the intensity of 100 W m-2. If the light of wavelength 400 nm is incident on the same material with an intensity of 1 W m-2, what would be the minimum reverse potential needed to stop the outflow of the electrons?
The maximum kinetic energy of the photoelectrons ejected will be ______ eV when the light of wavelength 350 nm is incident on a cesium surface. The work function of cesium = 1.9 eV.
A charged dust particle of radius 5 × 10-7 m is located in a horizontal electric field having an intensity of 6.28 × 105 V/m. The surrounding medium is air with a coefficient of viscosity η = 1.6 × 10-5 N-s/m2. If the particle moves with a uniform horizontal speed of 0.02 m/s, the number of electrons on it is ______.
For a given photosensitive material and frequency (> threshold frequency) of incident radiation, the photoelectric current varies with the intensity of incident light as:
Two radiations of photons energies 1 eV and 2.5 eV, successively illuminate a photosensitive metallic surface of work function 0.5 eV. The ratio of the maximum speeds of the emitted electrons is ______.
The following graphs show the variation of stopping potential corresponding to the frequency of incident radiation (ν) for a given metal. The correct variation is shown in graph [ν0 = threshold frequency].
|
(A) |
(B) |
|
(C) |
(D) |
Photoelectric emission is observed from a metallic surface for frequencies ν1 and ν2 of the incident light rays (ν1 > ν2). If the ratio of the maximum value of the kinetic energy of the photoelectrons emitted in the first case to that in the second case is 2 : K, then the threshold frequency of the metallic surface is ______.
By increasing the voltage in an electron diffraction tube, the radius of the diffraction rings will ______.
A parallel plate capacitor with air between the plates has capacitance 9 pF. The separation between the plates becomes thrice and the space between them is filled with a medium of dielectric constant 6. The capacitance becomes 'x' pF. The value of 'x' is ______.
