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A parallel beam of uniform monochromatic light of wavelength 2640 A has an intensity of 200 Watt per metre square. The no. of photons in 1 mm cube of this radiation are?
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A parallel beam of uniform monochromatic light of wavelength 2640 A ha...
Answer = 885
Intensity = power / area
given:
Area= 1× 10^-6 m^2
Intensity = 200 W m^-2
wavelength of photon = 2640 A•
energy of One photon = hc/wavelength of photon = 7.5×10^-19J
time = distance/velocity = 10^-3m/c
N = Intensity × area × time / energy of one photon
Intensity = power / area
given:
Area= 1× 10^-6 m^2
Intensity = 200 W m^-2
wavelength of photon = 2640 A•
energy of One photon = hc/wavelength of photon = 7.5×10^-19J
time = distance/velocity = 10^-3m/c
N = Intensity × area × time / energy of one photon
Community Answer
A parallel beam of uniform monochromatic light of wavelength 2640 A ha...
Understanding Photons and Light Intensity
To calculate the number of photons in a 1 mm³ cube of light radiation, we need to use the relationship between intensity, energy, and the properties of photons.
Step 1: Calculate Energy of a Single Photon
The energy \(E\) of a single photon can be calculated using the formula:
\[ E = \frac{hc}{\lambda} \]
- \(h\) (Planck's constant) = \(6.626 \times 10^{-34} \, \text{Js}\)
- \(c\) (speed of light) = \(3 \times 10^{8} \, \text{m/s}\)
- \(\lambda\) (wavelength) = \(2640 \, \text{Å} = 2640 \times 10^{-10} \, \text{m}\)
Calculating \(E\):
\[ E = \frac{(6.626 \times 10^{-34}) \times (3 \times 10^{8})}{2640 \times 10^{-10}} \approx 7.51 \times 10^{-19} \, \text{J} \]
Step 2: Calculate the Total Power in 1 mm³
Given the intensity \(I\) of the light is \(200 \, \text{W/m}^2\):
- The area of a 1 mm² surface is \(1 \times 10^{-6} \, \text{m}^2\).
- Power \(P\) in 1 mm³ is given by:
\[ P = I \times \text{Area} = 200 \times 1 \times 10^{-6} = 0.0002 \, \text{W} \]
Step 3: Calculate Number of Photons
To find the number of photons \(N\) in the power, we use:
\[ N = \frac{P}{E} \]
Substituting the values:
\[ N = \frac{0.0002}{7.51 \times 10^{-19}} \approx 2.66 \times 10^{14} \]
Conclusion
Thus, the number of photons in 1 mm³ of this radiation is approximately \(2.66 \times 10^{14}\).
To calculate the number of photons in a 1 mm³ cube of light radiation, we need to use the relationship between intensity, energy, and the properties of photons.
Step 1: Calculate Energy of a Single Photon
The energy \(E\) of a single photon can be calculated using the formula:
\[ E = \frac{hc}{\lambda} \]
- \(h\) (Planck's constant) = \(6.626 \times 10^{-34} \, \text{Js}\)
- \(c\) (speed of light) = \(3 \times 10^{8} \, \text{m/s}\)
- \(\lambda\) (wavelength) = \(2640 \, \text{Å} = 2640 \times 10^{-10} \, \text{m}\)
Calculating \(E\):
\[ E = \frac{(6.626 \times 10^{-34}) \times (3 \times 10^{8})}{2640 \times 10^{-10}} \approx 7.51 \times 10^{-19} \, \text{J} \]
Step 2: Calculate the Total Power in 1 mm³
Given the intensity \(I\) of the light is \(200 \, \text{W/m}^2\):
- The area of a 1 mm² surface is \(1 \times 10^{-6} \, \text{m}^2\).
- Power \(P\) in 1 mm³ is given by:
\[ P = I \times \text{Area} = 200 \times 1 \times 10^{-6} = 0.0002 \, \text{W} \]
Step 3: Calculate Number of Photons
To find the number of photons \(N\) in the power, we use:
\[ N = \frac{P}{E} \]
Substituting the values:
\[ N = \frac{0.0002}{7.51 \times 10^{-19}} \approx 2.66 \times 10^{14} \]
Conclusion
Thus, the number of photons in 1 mm³ of this radiation is approximately \(2.66 \times 10^{14}\).
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A parallel beam of uniform monochromatic light of wavelength 2640 A has an intensity of 200 Watt per metre square. The no. of photons in 1 mm cube of this radiation are?
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A parallel beam of uniform monochromatic light of wavelength 2640 A has an intensity of 200 Watt per metre square. The no. of photons in 1 mm cube of this radiation are? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A parallel beam of uniform monochromatic light of wavelength 2640 A has an intensity of 200 Watt per metre square. The no. of photons in 1 mm cube of this radiation are? covers all topics & solutions for JEE 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 Watt per metre square. The no. of photons in 1 mm cube of this radiation are?.
A parallel beam of uniform monochromatic light of wavelength 2640 A has an intensity of 200 Watt per metre square. The no. of photons in 1 mm cube of this radiation are? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A parallel beam of uniform monochromatic light of wavelength 2640 A has an intensity of 200 Watt per metre square. The no. of photons in 1 mm cube of this radiation are? covers all topics & solutions for JEE 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 Watt per metre square. The no. of photons in 1 mm cube of this radiation are?.
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