Advertisements
Advertisements
प्रश्न
A sphere of radius 1.00 cm is placed in the path of a parallel beam of light of large aperture. The intensity of the light is 0.5 W cm−2. If the sphere completely absorbs the radiation falling on it, Show that the force on the sphere due to the light falling on it is the same even if the sphere is not perfectly absorbing.
Advertisements
उत्तर
Consider a sphere of centre O and radius OP. As shown in the figure, the radius OP of the sphere is making an angle θ with OZ. Let us rotate the radius about OZ to get another circle on the sphere. The part of the sphere between the circle is a ring of area `2pir^2sin θdθ`.
Consider a small part of area `ΔA` of the ring at point P.
Energy of the light falling on this part in time `Δt` ,
`ΔU = I Δ t (ΔA cos θ)`
As the light is reflected by the sphere along PR, the change in momentum ,
`Δp = 2 (ΔU)/c cos θ = 2/c I Δ t (ΔA cos^2 θ)`
Therefore , the force will be
`(Δp)/(Δt) = 2/c I ΔA cos^2 θ`
The Component of force on ΔA , along ZO , is
`(Δp)/(Δt) cos θ = 2/c I ΔA cos^3 θ`
Now , force action on the ring,
`dF = 2/c I (2pir^2 sin θ dθ) cos^3 θ`
The force on the entire sphere ,
`F = ∫_0^(pi/2) (4pir^2I)/c cos^3 θ sin θ dθ`
= `- ∫_0^(pi/2) (4pir^2I)/c cos^3 θd(cos θ)`
= `(pir^2I)/c`
APPEARS IN
संबंधित प्रश्न
Define the term 'intensity of radiation' in terms of photon picture of light.
Is it always true that for two sources of equal intensity, the number of photons emitted in a given time are equal?
Can a photon be deflected by an electric field? Or by a magnetic field?
A hot body is placed in a closed room maintained at a lower temperature. Is the number of photons in the room increasing?
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 of light is used in a photoelectric effect. If the source is removed farther from the emitting metal, the stopping potential
A photon of energy hv is absorbed by a free electron of a metal with work-function hv − φ.
In which of the following situations, the heavier of the two particles has smaller de Broglie wavelength? The two particles
(a) move with the same speed
(b) move with the same linear momentum
(c) move with the same kinetic energy
(d) have fallen through the same height
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)
A beam of white light is incident normally on a plane surface absorbing 70% of the light and reflecting the rest. If the incident beam carries 10 W of power, find the force exerted by it on the surface.
(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.
The work function of a metal is 2.5 × 10−19 J. (a) Find the threshold frequency for photoelectric emission. (b) If the metal is exposed to a light beam of frequency 6.0 × 1014 Hz, what will be the stopping potential?
(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 work function of a photoelectric material is 4.0 eV. (a) What is the threshold wavelength? (b) Find the wavelength of light for which the stopping potential is 2.5 V.
(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 electric field associated with a light wave is given by `E = E_0 sin [(1.57 xx 10^7 "m"^-1)(x - ct)]`. Find the stopping potential when this light is used in an experiment on photoelectric effect with the emitter having work function 1.9 eV.
Define the term: threshold frequency
In photoelectric effect, the photoelectric current started to flow. This means that the frequency of incident radiations is ______.
Two monochromatic beams A and B of equal intensity I, hit a screen. The number of photons hitting the screen by beam A is twice that by beam B. Then what inference can you make about their frequencies?
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.
