Advertisements
Advertisements
प्रश्न
Consider an electron in front of metallic surface at a distance d (treated as an infinite plane surface). Assume the force of attraction by the plate is given as `1/4 q^2/(4πε_0d^2)`. Calculate work in taking the charge to an infinite distance from the plate. Taking d = 0.1 nm, find the work done in electron volts. [Such a force law is not valid for d < 0.1nm].
Advertisements
उत्तर
As per question F = `1/4 q^2/(4πε_0d^2)`
Let at any instant electron is at a distance x from the metal surface. Force of attraction between. metal surface and electron is F
F = `1/4 q^2/(4πε_0x^2)`
Work done by an external agency in taking the electron from distance d to ∞ is W.D. = `int_d^∞ F*dx`
W.D. = `int_d^∞ (q^2dx)/(4 xx 4πε_0x^2) = q^2/(4 xx 4πε_0) int_d^∞ x^-2 dx = q^2/(4 xx 4πε_0) x^-1/(-1)`
W.D. = `(-q^2)/(4.4πg e_0) [1/x]_d^∞ = (-q^2k)/4 [1/∞ - 1/d]`
W.D. = `(+ kq^2)/(4d)` [d = 0.1 nm = 10–10 m]
Work done is positive
So W.D. = `((1.6 xx 10^-19)^2 xx 9 xx 10^9)/(4 xx 10^-10)`
J = `(1.6 xx 9 xx 1.6 xx 10^(-33+9+10))/(4 xx 1.6 xx 10^-19)` eV
= `(9 xx 1.6 xx 10^(19+19))/4`
= 3.6 eV
APPEARS IN
संबंधित प्रश्न
The photoelectric work function for a metal surface is 2.3 eV. If the light of wavelength 6800A is incident on the surface of metal, find threshold frequency and incident frequency. Will there be an emission of photoelectrons or not?
[Velocity of light c = 3 x 108 m/s,
Planck’s constant, h = 6.63 * 10-34 Js ]
Write three characteristic features in photoelectric effect that cannot be explained on the basis of wave theory of light, but can be explained only using Einstein's equation.
Light of intensity ‘I’ and frequency ‘v’ is incident on a photosensitive surface and causes photoelectric emission. What will be the effect on anode current when (ii) the frequency of incident radiation is increased. In each case, all other factors remain the same. Explain, giving justification in each case.
Two monochromatic beams, one red and the other blue, have the same intensity. In which case (i) the number of photons per unit area per second is larger, (ii) the maximum kinetic energy of the photoelectrons is more? Justify your answer.
The graph shows the variation of stopping potential with frequency of incident radiation for two photosensitive metals A and B. Which one of the two has higher value of work-function? Justify your answer.
If the total energy of radiation of frequency 1014 Hz is 6.63 J, calculate the number of photons in the radiation. (Planck’s constant = 6.63 x 10–34 J.s.)
In an experiment of the photoelectric effect, the graph of maximum kinetic energy EK of the emitted photoelectrons versus the frequency v of the incident light is a straight line AB shown in Figure 6 below:
Find:
1) Threshold frequency of the metal
2) The work function of the metal.
3) Stopping potential for the photoelectrons emitted by the light of frequency `v = 30 xx 10^14 Hz`
A photosensitive surface emits photoelectrons when red light falls on it. Will the surface emit photoelectrons when blue light is incident on it? Give reason.
What change will you observe if intensity of incident radiation is changed but the frequency remains the same?
A beam of monochromatic radiation is incident on a photosensitive surface. Answer the following question giving reason :
Do the emitted photoelectrons have the same kinetic energy?
In photoelectric effect, why should the photoelectric current increase as the intensity of monochromatic radiation incident on a photosensitive surface is increased? Explain.
Draw a plot showing the variation of photoelectric current with collector plate potential for two different frequencies, v1 > v2, of incident radiation having the same intensity. In which case will the stopping potential be higher? Justify your answer.
What is photoelectri effect ? Defin (i) Stopping potential (ii) Photoelectric work function.
Calculate the momentum of a photon of energy 6 x I 0-19 J.
With reference to the photoelectric effect, what is meant by threshold wavelength?
Two metals A and B have work functions 4 eV and 6 eV respectively. Which metal has a lower threshold wavelength for photoelectric effect?
The phenomenon of photoelectric emission was observed by ______.
