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प्रश्न
Monochromatic radiation of wavelength 640.2 nm (1 nm = 10−9 m) from a neon lamp irradiates photosensitive material made of caesium on tungsten. The stopping voltage is measured to be 0.54 V. The source is replaced by an iron source and its 427.2 nm line irradiates the same photo-cell. Predict the new stopping voltage.
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उत्तर
Wavelength of the monochromatic radiation, λ = 640.2 nm = 640.2 × 10−9 m
Stopping potential of the neon lamp, V0 = 0.54 V
Charge on an electron, e = 1.6 × 10−19 C
Planck’s constant, h = 6.6 × 10−34 Js
Let `phi_0` be the work function and ν be the frequency of emitted light.
We have the photo-energy relation from the photoelectric effect as:
eV0 = hv − `phi_0`
`phi_0 = "hc"/lambda - "eV"_0`
= `(6.6 xx 10^(-34) xx 3 xx 10^8)/(640.2 xx 10^(-9)) - 1.6 xx 10^(-19) xx 0.54`
= `3.093 xx 10^(-19) - 0.864 xx 10^(-19)`
= `2.229 xx 10^(-19) "J"`
`= (2.229 xx 10^(-19))/(1.6 xx 10^(-19))`
= 1.39 eV
Wavelength of the radiation emitted from an iron source, λ' = 427.2 nm
= 427.2 × 10−9 m
Let `"V"_0^"'"` be the new stopping potential. Hence, photo-energy is given as:
`"eV"_0^"'" = "hc"/(lambda"'") - phi_0`
= `(6.6 xx 10^(-34) xx 3 xx 10^(8))/(427.2 xx 10^(-9)) - 2.229 xx 10^(-19)`
= `4.63 xx 10^(-19) - 2.229 xx 10^(-19)`
= `2.401 xx 10^(-19) "J"`
`= (2.401 xx 10^(-19))/(1.6 xx 10^(-19))`
= 1.5 eV
Hence, the new stopping potential is 1.50 eV.
संबंधित प्रश्न
The work function for the following metals is given:
Na: 2.75 eV; K: 2.30 eV; Mo: 4.17 eV; Ni: 5.15 eV
Which of these metals will not give photoelectric emission for a radiation of wavelength 3300 Å from a He-Cd laser placed 1 m away from the photocell? What happens if the laser is brought nearer and placed 50 cm away?
Every metal has a definite work function. Why do all photoelectrons not come out with the same energy if incident radiation is monochromatic? Why is there an energy distribution of photoelectrons?
Draw graphs showing variation of photoelectric current with applied voltage for two incident radiations of equal frequency and different intensities. Mark the graph for the radiation of higher intensity.
Can we find the mass of a photon by the definition p = mv?
Can a photon be deflected by an electric field? Or by a magnetic field?
It is found that photosynthesis starts in certain plants when exposed to sunlight, but it does not start if the plants are exposed only to infrared light. Explain.
A point source causes photoelectric effect from a small metal plate. Which of the following curves may represent the saturation photocurrent as a function of the distance between the source and the metal?
A photon of energy hv is absorbed by a free electron of a metal with work-function hv − φ.
The collector plate in an experiment on photoelectric effect is kept vertically above the emitter plate. A light source is put on and a saturation photocurrent is recorded. An electric field is switched on that has a vertically downward direction.
An atom absorbs a photon of wavelength 500 nm and emits another photon of wavelength 700 nm. Find the net energy absorbed by the atom in the process.
(Use h = 6.63 × 10-34J-s = 4.14 × 10-15 eV-s, c = 3 × 108 m/s and me = 9.1 × 10-31kg)
When the sun is directly overhead, the surface of the earth receives 1.4 × 103 W m−2 of sunlight. Assume that the light is monochromatic with average wavelength 500 nm and that no light is absorbed in between the sun and the earth's surface. The distance between the sun and the earth is 1.5 × 1011 m. (a) Calculate the number of photons falling per second on each square metre of earth's surface directly below the sun. (b) How many photons are there in each cubic metre near the earth's surface at any instant? (c) How many photons does the sun emit per second?
(Use h = 6.63 × 10-34J-s = 4.14 × 10-15 eV-s, c = 3 × 108 m/s and me = 9.1 × 10-31kg)
A 100 W light bulb is placed at the centre of a spherical chamber of radius 20 cm. Assume that 60% of the energy supplied to the bulb is converted into light and that the surface of the chamber is perfectly absorbing. Find the pressure exerted by the light on the surface of the chamber.
(Use h = 6.63 × 10-34J-s = 4.14 × 10-15 eV-s, c = 3 × 108 m/s and me = 9.1 × 10-31kg)
A totally reflecting, small plane mirror placed horizontally faces a parallel beam of light, as shown in the figure. The mass of the mirror is 20 g. Assume that there is no absorption in the lens and that 30% of the light emitted by the source goes through the lens. Find the power of the source needed to support the weight of the mirror.
(Use h = 6.63 × 10-34J-s = 4.14 × 10-15 eV-s, c = 3 × 108 m/s and me = 9.1 × 10-31kg)
Show that it is not possible for a photon to be completely absorbed by a free electron.
Define the term: threshold frequency
Define the terms "stopping potential' and 'threshold frequency' in relation to the photoelectric effect. How does one determine these physical quantities using Einstein's equation?
Explain how does (i) photoelectric current and (ii) kinetic energy of the photoelectrons emitted in a photocell vary if the frequency of incident radiation is doubled, but keeping the intensity same?
Show the graphical variation in the above two cases.
Consider a 20 W bulb emitting light of wavelength 5000 Å and shining on a metal surface kept at a distance 2 m. Assume that the metal surface has work function of 2 eV and that each atom on the metal surface can be treated as a circular disk of radius 1.5 Å.
- Estimate no. of photons emitted by the bulb per second. [Assume no other losses]
- Will there be photoelectric emission?
- How much time would be required by the atomic disk to receive energy equal to work function (2 eV)?
- How many photons would atomic disk receive within time duration calculated in (iii) above?
- Can you explain how photoelectric effect was observed instantaneously?
How would the stopping potential for a given photosensitive surface change if the frequency of the incident radiation were increased? Justify your answer.
