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प्रश्न
Read the following paragraph and answer the questions.
| The figure shows the variation of photoelectric current measured in a photocell circuit as a function of the potential difference between the plates of the photocell when light beams A, B, C and D of different wavelengths are incident on the photocell. Examine the given figure and answer the following questions: |
- Which light beam has the highest frequency and why?
- Which light beam has the longest wavelength and why?
- Which light beam ejects photoelectrons with maximum momentum and why?
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उत्तर
(i) We know that the stopping potential and frequency are related as
V = `((hf - phi))/q`
Where Φ is the work function defined as the amount of energy needed to bind the electrons in the metals, hf is the energy of photons, and q is the charge.
This relationship leads us to the conclusion that the greater negative the stopping potential, the higher the frequency. As a result, curve B has the highest frequency and the largest negative stopping potential in the graph.
(ii) We all know that the connection between wavelength and frequency is inverse. The wavelength reduces as the frequency rises and vice versa.
As can be seen from the graph, C has the lowest frequency out of all the possible values since its stopping potential is the least negative. Therefore, the wavelength is largest when the frequency is lowest. C has the longest wavelength as a result.
(iii) Highest momentum means highest kinetic energy which can be calculated with the help of velocity.
kinetic energy = `1/2mv^2`
Relation to the momentum, p2 = 2m(K.E.)
If kinetic energy is maximum, then momentum will be maximum.
We know that the stopping potential and frequency are related,
Vq = (hf - Φ)
The maximum kinetic energy of the electrons equals the stopping voltage when measured in electron volt. We can consider Φ as the kinetic energy.
Kinetic energy is maximum when the frequency is maximum and in the above part we have seen that it is maximum for curve B, so momentum is maximum for curve B.
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संबंधित प्रश्न
Use the same formula you employ in (a) to obtain electron speed for an collector potential of 10 MV. Do you see what is wrong? In what way is the formula to be modified?
Ultraviolet light of wavelength 2271 Å from a 100 W mercury source irradiates a photo-cell made of molybdenum metal. If the stopping potential is −1.3 V, estimate the work function of the metal. How would the photo-cell respond to a high intensity (∼105 W m−2) red light of wavelength 6328 Å produced by a He-Ne laser?
Can a photon be deflected by an electric field? Or by a magnetic field?
Let nr and nb be the number of photons emitted by a red bulb and a blue bulb, respectively, of equal power in a given time.
Calculate the number of photons emitted per second by a 10 W sodium vapour lamp. Assume that 60% of the consumed energy is converted into light. Wavelength of sodium light = 590 nm
(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)
The figure is the plot of stopping potential versus the frequency of the light used in an experiment on photoelectric effect. Find (a) the ratio h/e and (b) the work function.
Consider a thin target (10–2 cm square, 10–3 m thickness) of sodium, which produces a photocurrent of 100 µA when a light of intensity 100W/m2 (λ = 660 nm) falls on it. Find the probability that a photoelectron is produced when a photons strikes a sodium atom. [Take density of Na = 0.97 kg/m3].
Why it is the frequency and not the intensity of the light source that determines whether the emission of photoelectrons will occur or not? Explain.
How would the stopping potential for a given photosensitive surface change if the frequency of the incident radiation were increased? Justify your answer.
