Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
Sketch the graphs showing variation of stopping potential with frequency of incident radiations for two photosensitive materials A and B having threshold frequencies vA > vB.
(i) In which case is the stopping potential more and why?
(ii) Does the slope of the graph depend on the nature of the material used? Explain.
The photoelectric work function for a metal is 4.2 eV. If the stopping potential is 3V, find the threshold wavelength and maximum kinetic energy of emitted electrons.
(Velocity of light in air = 3 x 108m/s,
Planck's constant = 6·63 x10-34 J -s,
Charg.e ori electron = 1·6 x 10 -19 C)
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.
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.
The work functions for potassium and caesium are 2.25 eV and 2.14 eV respectively. Is the photoelectric effect possible for either of them if the incident wavelength is 5180 Å?
[Given : Planck’s constant = 6.63 x 10–34 J.s.;
Velocity of light = 3 x 108 m/s; 1 eV = 1.6 x 10–19 J]
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`
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?
A beam of monochromatic radiation is incident on a photosensitive surface. Answer the following question giving reason :
Does the kinetic energy of the emitted electrons depend on the intensity of incident radiation?
In photoelectric effect, why should the photoelectric current increase as the intensity of monochromatic radiation incident on a photosensitive surface is increased? Explain.
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.
Plot a labelled graph of IVsl where Vs is stopping potential versus frequency f of the incident radiation.
If the frequency of the incident radiation is increased from 4 × 1015 Hz to 8 × 1015 Hz, by how much will the stopping potential for a given photosensitive surface go up?
Photoelectric effect is possible ______.
