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प्रश्न
Define the terms (i) ‘cut-off voltage’ and (ii) ‘threshold frequency’ in relation to the phenomenon of photoelectric effect.
Using Einstein’s photoelectric equation shows how the cut-off voltage and threshold frequency for a given photosensitive material can be determined with the help of a suitable plot/graph.
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उत्तर
When light of sufficiently small wavelength is incident on a metal surface, electrons are ejected from the metal. This Phenomenon is called the photoelectric effect.
(i) The cathode is illuminated with light of some fixed frequency v and fixed Intensity I1. A small photoelectric current is observed due to few electrons that reach anode just because they have sufficiently large velocity of emission. If we made the potential of the anode negative with respect to cathode then the electrons emitted by cathode are repelled. Some electrons even go back to the cathode so that the current decreases. At a certain value of this negative potential, the current is completely stopped. The least value of this anode potential which just stops the photocurrent is called cut off potential or stopping potential.
(ii) For a given material, there is a certain minimum frequency that if the incident radiation has a frequency below this threshold, no photoelectric emission will take place, howsoever intense the radiation may be falling.
(iii) According to Einstein’s photoelectric equation, maximum K. E is given as
`K.E_(max) =(hc)/lambda phi = hv -phi`
Where λ is wavelength and ν is corresponding frequency and Φ is work function.
We expose a material to lights of various frequencies and thus photoelectric current is observed and cut off potential needed to reduce this current to Zero is noted. A graph is plotted and that is straight line.
At ν0 the stopping potential is zero this means at this frequency the incident light is not able to eject electrons this is threshold frequency. Extended this line gives the cut off potential to make the photo
current zero which is `(-phi)/e`
संबंधित प्रश्न
In an accelerator experiment on high-energy collisions of electrons with positrons, a certain event is interpreted as annihilation of an electron-positron pair of total energy 10.2 BeV into two γ-rays of equal energy. What is the wavelength associated with each γ-ray? (1BeV = 109 eV)
A small metal plate (work function φ) is kept at a distance d from a singly-ionised, fixed ion. A monochromatic light beam is incident on the metal plate and photoelectrons are emitted. Find the maximum wavelength of the light beam, so that some of the photoelectrons may go round the ion along a circle.
In a photoelectric experiment, the collector plate is at 2.0 V with respect to the emitter plate made of copper (φ = 4.5 eV). The emitter is illuminated by a source of monochromatic light of wavelength 200 nm. Find the minimum and maximum kinetic energy of the photoelectrons reaching the collector.
Consider the situation of the previous problem. Consider the faster electron emitted parallel to the large metal plate. Find the displacement of this electron parallel to its initial velocity before it strikes the large metal plate.
(Use h = 6.63 × 10-34J-s = 4.14 × 10-15 eV-s, c = 3 × 108 m/s and me = 9.1 × 10-31kg)
Use Einstein’s photoelectric equation to show how from this graph,
(i) Threshold frequency, and (ii) Planck’s constant can be determined.
According to Einstein's photoelectric equation, the plot of the kinetic energy of the emitted photoelectrons from a metal versus the frequency of the incident radiation gives a straight line, whose slope ______.
Each photon has the same speed but different ______.
The minimum energy required to remove an electron is called ______.
The photon emitted during the de-excitation from the first excited level to the ground state of a hydrogen atom is used to irradiate a photocathode in which the stopping potential is 5 V. Calculate the work function of the cathode used.
If c is the velocity of light in free space, the correct statements about photon among the following are:
- The energy of a photon is E = hv.
- The velocity of a photon is c.
- The momentum of a photon, ρ = `(h v)/c`.
- In a photon-electron collision, both total energy and total momentum are conserved.
- Photon possesses positive charge.
Choose the correct answer from the options given below:
