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The CMB contains roughly 400 million photons per m³. The energy of each photon depends on its wavelength. Calculate the typical wavelength of a CMB photon. Hint: The CMB is blackbody 3 x 106 radiation at a temperature of 2.73 K. According to Wien's law, the peak wavelength in nanometers is given by Amax (a) Calculate the wavelength at which the CMB is a maximum and, to make the units consistent, convert this wavelength from nanometers to meters. m

The CMB contains roughly 400 million photons per m³. The energy of each photon depends on its wavelength. Calculate the typical wavelength of a CMB photon. Hint: The CMB is blackbody 3 x 106 radiation at a temperature of 2.73 K. According to Wien's law, the peak wavelength in nanometers is given by Amax (a) Calculate the wavelength at which the CMB is a maximum and, to make the units consistent, convert this wavelength from nanometers to meters. m

College Physics
College Physics
1st Edition
ISBN:9781938168000
Author:Paul Peter Urone, Roger Hinrichs
Publisher:Paul Peter Urone, Roger Hinrichs
Chapter34: Frontiers Of Physics
Section: Chapter Questions
Problem 14PE: The peak intensity of the CMBR occurs at a wavelength of 1.1 mm. (a) What is the energy in eV at a...
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↓ C School SOLA webassign net Astronomy Textbook Microsoft Office Ho.. WebAssign The CMB contains roughly 400 million photons per m³. The energy of each photon depends on its wavelength. Calculate the typical wavelength of a CMB photon. Hint: The CMB is blackbody radiation at a temperature of 2.73 K. According to Wien's law, the peak wavelength in nanometers is given by Amax 3 x 106 T - Incognito (a) Calculate the wavelength at which the CMB is a maximum and, to make the units consistent, convert this wavelength from nanometers to meters.
Transcribed Image Text:↓ C School SOLA webassign net Astronomy Textbook Microsoft Office Ho.. WebAssign The CMB contains roughly 400 million photons per m³. The energy of each photon depends on its wavelength. Calculate the typical wavelength of a CMB photon. Hint: The CMB is blackbody radiation at a temperature of 2.73 K. According to Wien's law, the peak wavelength in nanometers is given by Amax 3 x 106 T - Incognito (a) Calculate the wavelength at which the CMB is a maximum and, to make the units consistent, convert this wavelength from nanometers to meters.
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Follow-up Question

Hello! can you please assist with D?

& For reference:

A = 0.0011 m

B = 1.807 x 10^-22 J

C = 7.228 x 10^-14 J/m^3

The CMB contains roughly 400 million photons per m³. The energy of each photon depends on its wavelength. Calculate the typical wavelength of a CMB photon. Hint: The CMB is blackbody radiation at a temperature of 2.73 K. According to Wien's law, the peak wavelength in nanometers is given by Amax 3 x 106 T (a) Calculate the wavelength at which the CMB is a maximum and, to make the units consistent, convert this wavelength from nanometers to meters. 0.0011 = (b) Following up on part (a), calculate the energy (in J) of a typical photon. Assume for this approximate calculation that each photon has the wavelength calculated in part (a). The energy of a photon is given by E = where h is Planck's constant and is equal to 6.626 x 10-34 J xs, c is the speed of light in m/s, and A is the wavelength in m. hc A 0.000000000000000 J J (c) Continuing the thinking in parts (a) and (b), calculate the energy in a cubic meter of space, multiply the energy per photon calculated in part (b) by the number of photons per cubic meter given above (Enter your answer in J/m³). 0.000000000000072 J/m³ (d) Continuing the thinking in the last three exercises, convert this energy to an equivalent in mass, use Einstein's equation E = mc2. Hint: Divide the energy per m³ calculated in part (c) by the speed of light squared. Check your units; you should have an answer in kg/m³. kg/m³
Transcribed Image Text:The CMB contains roughly 400 million photons per m³. The energy of each photon depends on its wavelength. Calculate the typical wavelength of a CMB photon. Hint: The CMB is blackbody radiation at a temperature of 2.73 K. According to Wien's law, the peak wavelength in nanometers is given by Amax 3 x 106 T (a) Calculate the wavelength at which the CMB is a maximum and, to make the units consistent, convert this wavelength from nanometers to meters. 0.0011 = (b) Following up on part (a), calculate the energy (in J) of a typical photon. Assume for this approximate calculation that each photon has the wavelength calculated in part (a). The energy of a photon is given by E = where h is Planck's constant and is equal to 6.626 x 10-34 J xs, c is the speed of light in m/s, and A is the wavelength in m. hc A 0.000000000000000 J J (c) Continuing the thinking in parts (a) and (b), calculate the energy in a cubic meter of space, multiply the energy per photon calculated in part (b) by the number of photons per cubic meter given above (Enter your answer in J/m³). 0.000000000000072 J/m³ (d) Continuing the thinking in the last three exercises, convert this energy to an equivalent in mass, use Einstein's equation E = mc2. Hint: Divide the energy per m³ calculated in part (c) by the speed of light squared. Check your units; you should have an answer in kg/m³. kg/m³
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Follow-up Question

Hi, can you please assist with C?

& For reference:

A = 0.0011 m

B = 1.807 x 10^-22 J

The CMB contains roughly 400 million photons per m³. The energy of each photon depends on its wavelength. Calculate the typical wavelength of a CMB photon. Hint: The CMB is blackbody radiation at a temperature of 2.73 K. According to Wien's law, the peak wavelength in nanometers is given by Amax 3 x 106 T (a) Calculate the wavelength at which the CMB is a maximum and, to make the units consistent, convert this wavelength from nanometers to meters. 0.0011 - (b) Following up on part (a), calculate the energy (in J) of a typical photon. Assume for this approximate calculation that each photon has the wavelength calculated in part (a). The energy of a photon is given by E = where h is Planck's constant and is equal to 6.626 x 10-34 J x s, c is the speed of light in m/s, and A is the wavelength in m. he A (c) 0.000000000000000 J Continuing the thinking in parts (a) and (b), calculate the energy in a cubic meter of space, multiply the energy per photon calculated in part (b) by the number of photons per cubic meter given above (Enter your answer in J/m³). J/m3
Transcribed Image Text:The CMB contains roughly 400 million photons per m³. The energy of each photon depends on its wavelength. Calculate the typical wavelength of a CMB photon. Hint: The CMB is blackbody radiation at a temperature of 2.73 K. According to Wien's law, the peak wavelength in nanometers is given by Amax 3 x 106 T (a) Calculate the wavelength at which the CMB is a maximum and, to make the units consistent, convert this wavelength from nanometers to meters. 0.0011 - (b) Following up on part (a), calculate the energy (in J) of a typical photon. Assume for this approximate calculation that each photon has the wavelength calculated in part (a). The energy of a photon is given by E = where h is Planck's constant and is equal to 6.626 x 10-34 J x s, c is the speed of light in m/s, and A is the wavelength in m. he A (c) 0.000000000000000 J Continuing the thinking in parts (a) and (b), calculate the energy in a cubic meter of space, multiply the energy per photon calculated in part (b) by the number of photons per cubic meter given above (Enter your answer in J/m³). J/m3
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Follow-up Question
(b) Following up on part (a), calculate the energy (in J) of a typical photon. Assume for this approximate calculation that each photon has the wavelength calculated in part (a). The hc where h is Planck's constant and is equal to 6.626 x 10-34 Jxs, c is the speed of light in m/s, and is the wavelength in m. energy of a photon is given by E = λ
Transcribed Image Text:(b) Following up on part (a), calculate the energy (in J) of a typical photon. Assume for this approximate calculation that each photon has the wavelength calculated in part (a). The hc where h is Planck's constant and is equal to 6.626 x 10-34 Jxs, c is the speed of light in m/s, and is the wavelength in m. energy of a photon is given by E = λ
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