NEET Exam > NEET Questions > Two metal spheres have radii r and 2r and the...
Start Learning for Free
Two metal spheres have radii r and 2r and they emit thermal radiation with maximum intensity at wavelength Lambda and 2 Lambda respectively. the respective ratio of the radiant energy emitted by them per second will be?
Most Upvoted Answer
Two metal spheres have radii r and 2r and they emit thermal radiation ...
Given: Two metal spheres of radii r and 2r respectively emit thermal radiation with maximum intensity at wavelength Lambda and 2 Lambda.
To Find: The ratio of radiant energy emitted by the spheres per second.
Solution:
Step 1: Calculate the wavelength of the emitted radiation from the spheres
The wavelength of the maximum intensity of the emitted radiation is given by Wien's displacement law:
λ_max = b/T
Where b is Wien's constant and T is the temperature of the object emitting the radiation.
Since both spheres are emitting radiation with maximum intensity at different wavelengths, they must be at different temperatures.
Let the temperature of the first sphere be T1 and the temperature of the second sphere be T2.
Thus, we have:
λ1 = b/T1 and λ2 = b/T2
Step 2: Find the ratio of the radiant energy emitted by the spheres per second
The radiant energy emitted per unit time by a body at a temperature T is given by the Stefan-Boltzmann law:
E = σT^4
Where σ is the Stefan-Boltzmann constant.
Thus, the ratio of the radiant energy emitted per second by the two spheres is given by:
E2/E1 = (σT2^4)/(σT1^4) = (T2/T1)^4
Using the expressions for λ1 and λ2 from Step 1, we have:
(T2/T1)^4 = (λ2/λ1)^4 = (2Lambda/Lambda)^4 = 16
Thus, the ratio of the radiant energy emitted per second by the two spheres is 16.
Answer: The ratio of the radiant energy emitted per second by the two spheres is 16.
To Find: The ratio of radiant energy emitted by the spheres per second.
Solution:
Step 1: Calculate the wavelength of the emitted radiation from the spheres
The wavelength of the maximum intensity of the emitted radiation is given by Wien's displacement law:
λ_max = b/T
Where b is Wien's constant and T is the temperature of the object emitting the radiation.
Since both spheres are emitting radiation with maximum intensity at different wavelengths, they must be at different temperatures.
Let the temperature of the first sphere be T1 and the temperature of the second sphere be T2.
Thus, we have:
λ1 = b/T1 and λ2 = b/T2
Step 2: Find the ratio of the radiant energy emitted by the spheres per second
The radiant energy emitted per unit time by a body at a temperature T is given by the Stefan-Boltzmann law:
E = σT^4
Where σ is the Stefan-Boltzmann constant.
Thus, the ratio of the radiant energy emitted per second by the two spheres is given by:
E2/E1 = (σT2^4)/(σT1^4) = (T2/T1)^4
Using the expressions for λ1 and λ2 from Step 1, we have:
(T2/T1)^4 = (λ2/λ1)^4 = (2Lambda/Lambda)^4 = 16
Thus, the ratio of the radiant energy emitted per second by the two spheres is 16.
Answer: The ratio of the radiant energy emitted per second by the two spheres is 16.
Community Answer
Two metal spheres have radii r and 2r and they emit thermal radiation ...
Attention NEET Students!
To make sure you are not studying endlessly, EduRev has designed NEET study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in NEET.
|
Explore Courses for NEET exam
|
|
Similar NEET Doubts
Top Courses for NEETView all
Two metal spheres have radii r and 2r and they emit thermal radiation with maximum intensity at wavelength Lambda and 2 Lambda respectively. the respective ratio of the radiant energy emitted by them per second will be?
Question Description
Two metal spheres have radii r and 2r and they emit thermal radiation with maximum intensity at wavelength Lambda and 2 Lambda respectively. the respective ratio of the radiant energy emitted by them per second will be? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two metal spheres have radii r and 2r and they emit thermal radiation with maximum intensity at wavelength Lambda and 2 Lambda respectively. the respective ratio of the radiant energy emitted by them per second will be? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two metal spheres have radii r and 2r and they emit thermal radiation with maximum intensity at wavelength Lambda and 2 Lambda respectively. the respective ratio of the radiant energy emitted by them per second will be?.
Two metal spheres have radii r and 2r and they emit thermal radiation with maximum intensity at wavelength Lambda and 2 Lambda respectively. the respective ratio of the radiant energy emitted by them per second will be? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two metal spheres have radii r and 2r and they emit thermal radiation with maximum intensity at wavelength Lambda and 2 Lambda respectively. the respective ratio of the radiant energy emitted by them per second will be? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two metal spheres have radii r and 2r and they emit thermal radiation with maximum intensity at wavelength Lambda and 2 Lambda respectively. the respective ratio of the radiant energy emitted by them per second will be?.
Solutions for Two metal spheres have radii r and 2r and they emit thermal radiation with maximum intensity at wavelength Lambda and 2 Lambda respectively. the respective ratio of the radiant energy emitted by them per second will be? in English & in Hindi are available as part of our courses for NEET.
Download more important topics, notes, lectures and mock test series for NEET Exam by signing up for free.
Here you can find the meaning of Two metal spheres have radii r and 2r and they emit thermal radiation with maximum intensity at wavelength Lambda and 2 Lambda respectively. the respective ratio of the radiant energy emitted by them per second will be? defined & explained in the simplest way possible. Besides giving the explanation of
Two metal spheres have radii r and 2r and they emit thermal radiation with maximum intensity at wavelength Lambda and 2 Lambda respectively. the respective ratio of the radiant energy emitted by them per second will be?, a detailed solution for Two metal spheres have radii r and 2r and they emit thermal radiation with maximum intensity at wavelength Lambda and 2 Lambda respectively. the respective ratio of the radiant energy emitted by them per second will be? has been provided alongside types of Two metal spheres have radii r and 2r and they emit thermal radiation with maximum intensity at wavelength Lambda and 2 Lambda respectively. the respective ratio of the radiant energy emitted by them per second will be? theory, EduRev gives you an
ample number of questions to practice Two metal spheres have radii r and 2r and they emit thermal radiation with maximum intensity at wavelength Lambda and 2 Lambda respectively. the respective ratio of the radiant energy emitted by them per second will be? tests, examples and also practice NEET tests.
|
|
Explore Courses for NEET exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup