Advertisements
Advertisements
प्रश्न
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)
Advertisements
उत्तर
Here,
Intensity of light, `l = 1.4 × 10^3` W/m2,
Wavelength of light, `λ = 500 "nm" = 500 xx 10^-9 "m"`
Distance between the Sun and Earth, `l = 1.5 xx 10^11 "m"`
Intensity,
`I = "power"/"Area" = 1.4 xx 10^3 "W/m"^2`
Let n be the number of photons emitted per second.
∴ Power, P = Energy emitted/second
`P = (nhc)/λ`,
where λ = wavelength of light
h = Planck's constant
c = speed of light
Number of photons/`"m"^2` = `(nhc)/(λ xx A) = (nhc)/(λ xx 1) = l`
`therefore n = (I xx λ)/(hc)`
= `(1.4 xx 10^3 xx 500 xx 10^-9)/(6.63 xx 10^-34 xx 3 xx 10^8)`
= `3.5 xx 10^21`
(b) Consider number of two parts at a distance r and r + dr from the source.
Let dt' be the time interval in which the photon travels from one part to another.
Total number of photons emitted in this time interval,
`N = ndt = ((Pλ)/(hc xx A))(dr)/c`
These points will be between two spherical shells of radius 'r' and r + dr. It will be the distance of the 1st point from the sources.
In this case,
`l = 1.5 xx 10^11 "m"`
`"Wavelength" , λ = 500 "nm" = 500 xx 10^-9 "m"`
`P/(4pir^2) = 1.4 xx 10^3`
∴ No. of photons `/"m"^3 = P/(4pir^2) λ/(hc^2)`
= `1.4 xx 10^3 xx (500 xx 10^-9)/(6.63 xx 10^-34 xx 9 xx 10^16`
= `1.2 xx 10^13`
(c) Number of photons emitted = (Number of photons / s-m2) × Area
= `(3.5 xx 10^21) xx 4pil^2`
= `3.5 xx 10^21 xx 4 xx (3.14) xx (1.5 xx 10^11)^2`
= `9.9 xx 10^44`
APPEARS IN
संबंधित प्रश्न
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?
Can we find the mass of a photon by the definition p = mv?
What is the speed of a photon with respect to another photon if (a) the two photons are going in the same direction and (b) they are going in opposite directions?
If the wavelength of light in an experiment on photoelectric effect is doubled,
(a) photoelectric emission will not take place
(b) photoelectric emission may or may not take place
(c) the stopping potential will increase
(d) the stopping potential will decrease
Calculate the momentum of a photon of light of wavelength 500 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)
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)
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)
The electric field associated with a monochromatic beam is 1.2 × 1015 times per second. Find the maximum kinetic energy of the photoelectrons when this light falls on a metal surface whose work function is 2.0 eV.
(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.
A small piece of cesium metal (φ = 1.9 eV) is kept at a distance of 20 cm from a large metal plate with a charge density of 1.0 × 10−9 C m−2 on the surface facing the cesium piece. A monochromatic light of wavelength 400 nm is incident on the cesium piece. Find the minimum and maximum kinetic energy of the photoelectrons reaching the large metal plate. Neglect any change in electric field due to the small piece of cesium present.
(Use h = 6.63 × 10-34J-s = 4.14 × 10-15 eV-s, c = 3 × 108 m/s and me = 9.1 × 10-31kg)
On the basis of the graphs shown in the figure, answer the following questions :
(a) Which physical parameter is kept constant for the three curves?
(b) Which is the highest frequency among v1, v2, and v3?
In the case of photoelectric effect experiment, explain the following facts, giving reasons.
The photoelectric current increases with increase of intensity of incident light.
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?
The work function for a metal surface is 4.14 eV. The threshold wavelength for this metal surface is ______.
Plot a graph showing the variation of photoelectric current, as a function of anode potential for two light beams having the same frequency but different intensities I1 and I2 (I1 > I2). Mention its important features.
A metallic plate exposed to white light emits electrons. For which of the following colours of light, the stopping potential will be maximum?
- Assertion (A): For the radiation of a frequency greater than the threshold frequency, the photoelectric current is proportional to the intensity of the radiation.
- Reason (R): Greater the number of energy quanta available, the greater the number of electrons absorbing the energy quanta and the greater the number of electrons coming out of the metal.
