(a)
Interpretation:
The total energy output must be calculated for the blackbody heated at 4500 K.
Concept introduction:
Stefan’s law essentially states that the total quantity of heat energy released by a perfect blackbody per unit area per second is directly proportional to the absolute temperature’s fourth power of its surface given by the equation-
Wein’s displacement Law which states that the maximum wavelength in micrometers for the radiations of the blackbody is given by:
Where,
T = temperature in Kelvin
Answer to Problem 7.4QAP
The amount of energy emitted by Et at temperature 4500K is
Explanation of Solution
The total energy Et emitted per unit time per unit area is calculated by:
Given that-
T = 4500K
The value of total energy Et is:
Thus, the total amount of energy emitted Et at 4500 K is
(b)
Interpretation:
The total energy output must be calculated for the blackbody heated at 2500 K.
Concept introduction:
Stefan’s law essentially states that the total quantity of heat energy released by a perfect blackbody per unit area per second is directly proportional to the absolute temperature’s fourth power of its surface given by the equation-
Wein’s displacement Law which states that the maximum wavelength in micrometers for the radiations of the blackbody is given by:
Where,
T = temperature in Kelvin
Answer to Problem 7.4QAP
The amount of energy emitted by Et at temperature 2500K is
Explanation of Solution
The total energy Et emitted per unit time per unit area is calculated by:
Given that-
T = 2500K
The value of total energy Et is:
Thus, the total amount of energy emitted Et at 2500 K is
(c)
Interpretation:
The total energy output must be calculated for the blackbody heated at 1250K.
Concept introduction:
Stefan’s law essentially states that the total quantity of heat energy released by a perfect blackbody per unit area per second is directly proportional to the absolute temperature’s fourth power of its surface given by the equation-
Wein’s displacement Law which states that the maximum wavelength in micrometers for the radiations of the blackbody is given by:
Where,
T = temperature in Kelvin
Answer to Problem 7.4QAP
The amount of energy emitted by Et at temperature 1250K is
Explanation of Solution
The total energy Et emitted per unit time per unit area is calculated by:
Given that-
T = 1250K
The value of total energy Et is:
Thus, the total amount of energy emitted Et at 1250 K is
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Chapter 7 Solutions
Principles of Instrumental Analysis
- Describe the differences and similarities between spontaneous and stimulated emission.arrow_forward(c) The kinetic energy, K₁, of electrons emitted from a metal surface after irradiation with UV light of wavelength λ is given by: hc Kg = -4 where his Planck's constant (6.626 x 10-4 Js), c is the speed of light in a vacuum (2.99 x 108 m s¹), and is the work function of the metal surface. In a specific experiment, light with a wavelength of 266 nm was used to irradiate a cadmium (Cd) metal surface.arrow_forward(c) The kinetic energy, KE, of electrons emitted from a metal surface after irradiation with UV light of wavelength A is given by: hc Kε = 7-9 where h is Planck's constant (6.626 x 10-4 Js), c is the speed of light in a vacuum (2.99 x 108 m s¹), and is the work function of the metal surface. In a specific experiment, light with a wavelength of 266 nm was used to irradiate a cadmium (Cd) metal surface. Calculate the photon energy of the light used in the experiment, in Joules. (1) ₂4arrow_forward
- Calculate the momentum of an X-ray photon with a wavelength of 0.17nm. How does this value compare with the momentum of a free electron that has been accelerated through a potential difference of 5000 volts? (Hint: electron mass, m, = 9.10938 x 10" kg; electron charge e = 1.602 x 10"C; speed of light e = 3.0 x 10* m.s'; 1.00 J= 1.00 VC; h = 6.626 x 10"J.s. The various energy units are: 1 J= 1 kg.m°s³, 1.00 eV =1VC, leV= 1.602 x 10"J, 1J= 6.242 x 10" eV, etc.). %3Darrow_forward4-68. At noon on a clear day, sunlight reaches the earth's surface at Madison, Wisconsin, with an aver- age power of approximately 1.0 kJ.sm2. If the sun- light consists of photons with an average wavelength of 510 nm, how many photons strike a 1.0-cm² area per second?arrow_forwardCalculate the momentum of an X-ray photon with a wavelength of 0.17nm. How does this value compare with the momentum of a free electron that has been accelerated through a potential difference of 5000 volts? (Hint: electron mass, m, = 9.10938 x 10" kg; electron charge e = 1.602 x 10"C; speed of light e = 3.0 x 10° m.s'; 1.00 J= 1.00 VC; h = 6.626 x 10"J.s. The various energy units are: 1 J=1 kg.m's", 1.00 cV =1VC, leV = 1.602 x 10"J, 1J=6.242 x 10" eV, etc.). %3D %3Darrow_forward
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- Consider an Ar atom trapped in square box with length 1 m. Assume that the energy of the Ar atom is equal to thermal energy: 3kBT/2 at 25 degrees Celsius. a)Use the model of a particle in a box and assume the particle is at the state: n = nx = ny = nz , calculate n of the above system. b) What is the energy separation between the states (n, n, n) and (n + 1, n, n). c) Assume that all the energy of the particle is from kinetic energy. Calculate the de Broglie wavelength of the particle. d) Based on your answers above, would you treat this particle classically or quantumly? Explain your answer.arrow_forward5) Richard Feynman called the Euler relation the most remarkable formula in mathematics. Use the Euler relation to give the value of the following quantities. eio=1 ein/2_ ein = ei2π = (Hix = (rcosx = i sin x)arrow_forwardpart d Consider an Ar atom trapped in square box with length 1 m. Assume that the energy of the Ar atom is equal to thermal energy: 3kBT/2 at 250C. a) Use the model of a particle in a box and assume the particle is at the state: n = nx = ny = nz, calculate n of the above system. b) What is the energy separation between the states (n, n, n) and (n + 1, n, n). c) Assume that all the energy of the particle is from kinetic energy. Calculate the de Broglie wavelength of the particle. d) Based on your answers above, would you treat this particle classically or quantumly? Explain your answer.arrow_forward
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