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?

Consider a 20 W bulb emitting light of wavelength 5000 Å and shining on a metal surface kept at a distance 2 m.

प्रश्न

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?

दीर्घउत्तर

उत्तर

According to the problem, P = 20 W, λ = 5000 Å = 5000 × 10^–10 m, distance (d) = 2 m, work function `phi_0` = 2 eV, radius r = 1.5 Å = 1.5 × 10^–10 m

Now, Number of photon emitted by bulb per second, n' = `(dN)/(dt)`

i. Number of photon emitted by bulb per second is n’ = `(P)/((hc)/λ) = (Pλ)/(hc)`

= `(20 xx (5000 xx 10^-10))/((6.62 xx 10^-34) xx (3 xx 10^8))`

⇒ n' = 5 × 10¹⁹/sec

ii. Energy of the incident photon = `(hc)/λ`

= `((6.62 xx 10^-34) xx (3 xx 10^8))/(5000 xx 10^-10 xx 1.6 xx 10^-19)`

= 2.48 ev

As this energy is greater than 2 eV (i.e., a work function of the metal surface), hence photoelectric emission takes place.

iii. Let Δt be the time spent in getting the energy `phi` = (work function of metal).

Consider the figure, if P is the power of source then energy received by the atomic disc

`p/(4πd^2) xx pir^2Δt = phi_0`

⇒ Δt = `(4phi_0d^2)/(Pr^2)`

= `(4 xx (2 xx 1.6 xx 10^-19) xx 2^2)/(20 xx (1.5 xx 10^-10)^2`

= 2.84 s

iv. Number of photons received by the atomic disc in time Δt is

N = `(n^' xx pir^2)/(4pid^2) xx Δt`

= `(n^'r^2Δt)/(4d^2)`

= `((5 xx 10^19) xx (1.5 xx 10^-10)^2 xx 28.4)/(4 xx (2)^2`

= 2

Now let us discuss the last part in detail. As the time of emission of electrons is 11.04 s.

v. In photoelectric emission, there is a collision between the incident photon and free electron of the metal surface, which lasts for a very short interval of time (≈ 10^–9 s), hence we say photoelectric emission is instantaneous.

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Experimental Study of Photoelectric Effect

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Q 11.29 Q 11.28 Next

पाठ 11: Dual Nature Of Radiation And Matter - Exercises [पृष्ठ ७४]

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एनसीईआरटी एक्झांप्लर Physics Exemplar [English] Class 12

पाठ 11 Dual Nature Of Radiation And Matter
Exercises | Q 11.29 | पृष्ठ ७४

संबंधित प्रश्‍न

(a) Estimate the speed with which electrons emitted from a heated emitter of an evacuated tube impinge on the collector maintained at a potential difference of 500 V with respect to the emitter. Ignore the small initial speeds of the electrons. The specific charge of the electron, i.e., its e/m is given to be 1.76 × 10¹¹ C kg⁻¹.

(b) 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?

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?

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.

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If an electron has a wavelength, does it also have a colour?

Let n_r and n_b be the number of photons emitted by a red bulb and a blue bulb, respectively, of equal power in a given time.

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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