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A parallel beam of uniform, monochromatic light of wavelength 2640 A has an intensity of 200 W/m2. The number of photons in 1 mm3 of this radiation are ...............
Correct answer is '885'. Can you explain this answer?
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Verified Answer
A parallel beam of uniform, monochromatic light of wavelength 2640 A h...
I=nhv/ΔtA=[N.h(C/ λ)]/(1mm/c)x(1mm2)
N=200x10-9x2640x10-10/(3x108)2x6.63x10-34
=885 Photons/mm3
N=200x10-9x2640x10-10/(3x108)2x6.63x10-34
=885 Photons/mm3
Most Upvoted Answer
A parallel beam of uniform, monochromatic light of wavelength 2640 A h...
Given:
- Wavelength of light, λ = 2640 A = 2640 x 10^(-10) m
- Intensity of light, I = 200 W/m^2
- Volume of light, V = 1 mm^3 = 1 x 10^(-9) m^3
To find:
Number of photons in 1 mm^3 of this radiation
Solution:
The energy of a photon is given by the equation:
E = hc/λ
where,
- h is the Planck's constant (6.63 x 10^(-34) J.s)
- c is the speed of light (3 x 10^8 m/s)
- λ is the wavelength of light
Step 1: Calculate the energy of a single photon:
E = (6.63 x 10^(-34) J.s x 3 x 10^8 m/s) / (2640 x 10^(-10) m)
E = 7.5 x 10^(-19) J
Step 2: Calculate the number of photons:
Given that the intensity of light is 200 W/m^2, we can relate it to the energy of a single photon using the equation:
Intensity = Energy x Number of photons x Frequency
Frequency = c/λ
where,
- Intensity is in watts per square meter (W/m^2)
- Energy is in joules (J)
- Number of photons is the quantity we need to find
- Frequency is in hertz (Hz)
We can rewrite the equation as:
Intensity = Energy x Number of photons x c/λ
Simplifying and rearranging the equation:
Number of photons = Intensity x λ / (Energy x c)
Number of photons = (200 W/m^2) x (2640 x 10^(-10) m) / (7.5 x 10^(-19) J x 3 x 10^8 m/s)
Step 3: Calculate the number of photons in 1 mm^3 of light:
Volume of light = 1 x 10^(-9) m^3
Number of photons in 1 mm^3 = Number of photons x Volume of light
Number of photons in 1 mm^3 = [(200 W/m^2) x (2640 x 10^(-10) m) / (7.5 x 10^(-19) J x 3 x 10^8 m/s)] x (1 x 10^(-9) m^3)
Simplifying the equation:
Number of photons in 1 mm^3 = 2.96 x 10^(15)
Therefore, the correct answer is 885 (approximately)
- Wavelength of light, λ = 2640 A = 2640 x 10^(-10) m
- Intensity of light, I = 200 W/m^2
- Volume of light, V = 1 mm^3 = 1 x 10^(-9) m^3
To find:
Number of photons in 1 mm^3 of this radiation
Solution:
The energy of a photon is given by the equation:
E = hc/λ
where,
- h is the Planck's constant (6.63 x 10^(-34) J.s)
- c is the speed of light (3 x 10^8 m/s)
- λ is the wavelength of light
Step 1: Calculate the energy of a single photon:
E = (6.63 x 10^(-34) J.s x 3 x 10^8 m/s) / (2640 x 10^(-10) m)
E = 7.5 x 10^(-19) J
Step 2: Calculate the number of photons:
Given that the intensity of light is 200 W/m^2, we can relate it to the energy of a single photon using the equation:
Intensity = Energy x Number of photons x Frequency
Frequency = c/λ
where,
- Intensity is in watts per square meter (W/m^2)
- Energy is in joules (J)
- Number of photons is the quantity we need to find
- Frequency is in hertz (Hz)
We can rewrite the equation as:
Intensity = Energy x Number of photons x c/λ
Simplifying and rearranging the equation:
Number of photons = Intensity x λ / (Energy x c)
Number of photons = (200 W/m^2) x (2640 x 10^(-10) m) / (7.5 x 10^(-19) J x 3 x 10^8 m/s)
Step 3: Calculate the number of photons in 1 mm^3 of light:
Volume of light = 1 x 10^(-9) m^3
Number of photons in 1 mm^3 = Number of photons x Volume of light
Number of photons in 1 mm^3 = [(200 W/m^2) x (2640 x 10^(-10) m) / (7.5 x 10^(-19) J x 3 x 10^8 m/s)] x (1 x 10^(-9) m^3)
Simplifying the equation:
Number of photons in 1 mm^3 = 2.96 x 10^(15)
Therefore, the correct answer is 885 (approximately)
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A parallel beam of uniform, monochromatic light of wavelength 2640 A h...
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A parallel beam of uniform, monochromatic light of wavelength 2640 A has an intensity of 200 W/m2. The number of photons in 1 mm3of this radiation are ...............Correct answer is '885'. Can you explain this answer?
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A parallel beam of uniform, monochromatic light of wavelength 2640 A has an intensity of 200 W/m2. The number of photons in 1 mm3of this radiation are ...............Correct answer is '885'. Can you explain this answer? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A parallel beam of uniform, monochromatic light of wavelength 2640 A has an intensity of 200 W/m2. The number of photons in 1 mm3of this radiation are ...............Correct answer is '885'. Can you explain this answer? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A parallel beam of uniform, monochromatic light of wavelength 2640 A has an intensity of 200 W/m2. The number of photons in 1 mm3of this radiation are ...............Correct answer is '885'. Can you explain this answer?.
A parallel beam of uniform, monochromatic light of wavelength 2640 A has an intensity of 200 W/m2. The number of photons in 1 mm3of this radiation are ...............Correct answer is '885'. Can you explain this answer? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A parallel beam of uniform, monochromatic light of wavelength 2640 A has an intensity of 200 W/m2. The number of photons in 1 mm3of this radiation are ...............Correct answer is '885'. Can you explain this answer? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A parallel beam of uniform, monochromatic light of wavelength 2640 A has an intensity of 200 W/m2. The number of photons in 1 mm3of this radiation are ...............Correct answer is '885'. Can you explain this answer?.
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