Advertisements
Advertisements
प्रश्न
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].
Advertisements
उत्तर
According to the problem, the area of the target A = 10–2 cm2 = 10–4 m2
And thickness, d = 10–3 m
Photocurrent, i = 100 × 10–6 A= 10–4 A
Intensity, I = 100 W/m2
⇒ λ = 660 nm = 660 × 10–9 m
ρNa = 0.97 kg/m3
Avogadro number = 6 × 1026 kg atom
Volume of sodium target = A × d
= 10–4 × 10–3
= 10–7 m3
We know that 6 × 1026 atoms of sodium weigh = 23 kg
Density of sodium = 0.97 kg/m3
Hence the volume of 6 × 1026 sodium atoms = `23/0.97` m3
Volume occupied by one sodium atom = `23/(0.97 xx (6 xx 10^36))` = 3.95 × 10–26 m3
Number of sodium atoms in target `(N_"sodium") = 10^-7/(3.95 xx 10^-26)` = 2.53 × 1018
Let m be the number of photons falling per second on the target.
Energy of each photon = `(hc)/A`
Total energy falling per second on target = `(nhc)/λ = IA`
∴ `n = (IAλ)/(hc)`
= `(100 xx 10^-4 xx (660 xx 10^-9))/((6.62 xx 10^-34) xx (3 xx 10^8))` = 3.3 × 1016
Let P be the probability of emission per atom per photon. The number of photoelectrons emitted per second
`N = P xx n xx (N_"sodium")`
= `P xx (33 xx 10^16) xx (2.53 xx 10^18)`
Now, according to the question,
i = 100 µA = 100 × 10–6 = 10–4 A
Current, i = Ne
∴ `10^-4 xx P xx (3.3 xx 10^16) xx (2.53 xx 10^18) xx (1.6 xx 10^-19)`
⇒ `P = 10^-4/((3.3 xx 10^16) xx (2.53 xx 10^18) xx (1.6 xx 10^-19))`
= 7.48 × 10–21
Then, the probability of photoemission by a single photon on a single atom is very much less than 1. Because the absorption of two photons by an atom is negligible.
APPEARS IN
संबंधित प्रश्न
The photoelectric cut-off voltage in a certain experiment is 1.5 V. What is the maximum kinetic energy of photoelectrons emitted?
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?
Monochromatic radiation of wavelength 640.2 nm (1 nm = 10−9 m) from a neon lamp irradiates photosensitive material made of caesium on tungsten. The stopping voltage is measured to be 0.54 V. The source is replaced by an iron source and its 427.2 nm line irradiates the same photo-cell. Predict the new stopping voltage.
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?
Should the energy of a photon be called its kinetic energy or its internal energy?
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?
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)
An atom absorbs a photon of wavelength 500 nm and emits another photon of wavelength 700 nm. Find the net energy absorbed by the atom in the process.
(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)
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, find the force exerted by the light beam on the sphere.
(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 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.
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)
Define the term: threshold frequency
In the case of photoelectric effect experiment, explain the following facts, giving reasons.
The photoelectric current increases with increase of intensity of incident light.
Do all the electrons that absorb a photon come out as photoelectrons?
The graph shows the variation of photocurrent for a photosensitive metal
- What does X and A on the horizontal axis represent?
- Draw this graph for three different values of frequencies of incident radiation ʋ1, ʋ2 and ʋ3 (ʋ3 > ʋ2 > ʋ1) for the same intensity.
- Draw this graph for three different values of intensities of incident radiation I1, I2 and I3 (I3 > I2 > I1) having the same frequency.
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?
The figure shows a plot of stopping potential (V0) versus `1/lambda`, where λ is the wavelength of the radiation causing photoelectric emission from a surface. The slope of the line is equal to ______.
