Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
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?
It is found that yellow light does not eject photoelectrons from a metal. Is it advisable to try with orange light or with green light?
The threshold wavelength of a metal is λ0. Light of wavelength slightly less than λ0 is incident on an insulated plate made of this metal. It is found that photoelectrons are emitted for some time and after that the emission stops. Explain.
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.
If the frequency of light in a photoelectric experiment is doubled, the stopping potential will ______.
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)
A parallel beam of monochromatic light of wavelength 663 nm is incident on a totally reflecting plane mirror. The angle of incidence is 60° and the number of photons striking the mirror per second is 1.0 × 1019. Calculate the force exerted by the light beam on 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.
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.
(Use h = 6.63 × 10-34J-s = 4.14 × 10-15 eV-s, c = 3 × 108 m/s and me = 9.1 × 10-31kg)
Define the term: threshold frequency
Answer the following question.
Plot a graph of photocurrent versus anode potential for radiation of frequency ν and intensities I1 and I2 (I1 < I2).
In the case of photoelectric effect experiment, explain the following facts, giving reasons.
The photoelectric current increases with increase of intensity of incident light.
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.
In photoelectric effect, the photoelectric current started to flow. This means that the frequency of incident radiations is ______.
If photons of ultraviolet light of energy 12 eV are incident on a metal surface of work function of 4 eV, then the stopping potential (in eV) will be :
What is the effect of threshold frequency and stopping potential on increasing the frequency of the incident beam of light? Justify your answer.
Which of the following options represents the variation of photoelectric current with property of light shown on the x-axis?
