General Physics, 2nd Edition
2nd Edition
ISBN: 9780471522782
Author: Morton M. Sternheim
Publisher: WILEY
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Chapter 26, Problem 12E
(a)
To determine
The wavelength at
(b)
To determine
The corresponding frequency for
(c)
To determine
The corresponding frequency for
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To measure temperatures, physicists often use the variation of intensity of EM radiation emitted by an object. The wavelength at which the intensity is greatest is given by the equation:
λmaxT = 0.2898 cm.K
where λmax is the wavelength of greatest intensity and T is the temperature of the object in kelvins. In 1965, microwave radiation peaking at λmax = 0.107 cm was discovered coming in all directions from space. To what temperature, in a) K b) °C c) °F, does this wavelength correspond?
An infrared satellite measures outgoing radiation that leaves Earth's surface through an atmospheric window. The observed spectral irradiance at a wavelength of 10 μm is 2.199×107 W m-2 m-1. What is the temperature of the surface? Give your answer in K.
A particular star has a radius of 8.46 ✕ 108 m. The peak intensity of the radiation it emits is at a wavelength of 679 nm.
(a) What is the energy (in J) of a photon with this wavelength?
answer in J
(b) What is the star's surface temperature (in K)? (Round your answer to at least the nearest integer.)
answer in K
(c) At what rate (in W) is energy emitted from the star in the form of radiation? Assume the star is a blackbody, with emissivity
e = 1.
answer in W
(d) Using the results from parts (a) and (c), estimate the rate (in photons/s) at which photons are emitted by the star.
answer in photon/s
Chapter 26 Solutions
General Physics, 2nd Edition
Ch. 26 - Prob. 1RQCh. 26 - Prob. 2RQCh. 26 - Prob. 3RQCh. 26 - Prob. 4RQCh. 26 - Prob. 5RQCh. 26 - Prob. 6RQCh. 26 - Prob. 7RQCh. 26 - Prob. 1ECh. 26 - Prob. 2ECh. 26 - Prob. 3E
Ch. 26 - Prob. 4ECh. 26 - Prob. 5ECh. 26 - Prob. 6ECh. 26 - Prob. 7ECh. 26 - Prob. 8ECh. 26 - Prob. 9ECh. 26 - Prob. 10ECh. 26 - Prob. 11ECh. 26 - Prob. 12ECh. 26 - Prob. 13ECh. 26 - Prob. 14ECh. 26 - Prob. 15ECh. 26 - Prob. 16ECh. 26 - Prob. 17ECh. 26 - Prob. 18ECh. 26 - Prob. 19ECh. 26 - Prob. 20ECh. 26 - Prob. 21ECh. 26 - Prob. 22ECh. 26 - Prob. 23ECh. 26 - Prob. 24ECh. 26 - Prob. 25ECh. 26 - Prob. 26ECh. 26 - Prob. 27ECh. 26 - Prob. 28ECh. 26 - Prob. 29ECh. 26 - Prob. 30ECh. 26 - Prob. 31ECh. 26 - Prob. 32ECh. 26 - Prob. 33ECh. 26 - Prob. 34E
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- The incident radiation on the earth's surface can be approximated by Ii = In cos 0, where In = 80 W/m2. sr is the total radiation intensity directed perpendicular to the surface. What is the total irradiation at the surface of the earth?arrow_forwardProblem-1: An asteroid is hurtling toward earth at 150,000“. The temperature of the asteroid is about 100 K, meaning that its peak emission is 2 = 29 µm. The speed of light is c = 3E[8]. a) What is the wavelength of light that we receive from the asteroid? (Answer: 2.89855E[-05] m)arrow_forwardYou are using a radiometer to observe the thermal radi- ation from an object that is heated to maintain its tem- perature at 1278 K. The radiometer records radiation in a wavelength interval of 12.6 nm. By changing the wave- length at which you are measuring, you set the radiome- ter to record the most intense radiation emission from the object. What is the intensity of the emitted radiation in this interval?arrow_forward
- A small body is placed inside of a spherical stainless steel chamber with a diameter of 3 m. The chamber is evacuated and has a constant surface temperature of 500 K. Determine the radiation incident on the surface of the small body inside the chamber if the interior surface of the chamber is (a) coated black and (b) well-polished.arrow_forwardA blackbody is a substance that absorbs radiation of all wavelengths and radiates in a continuous spectrum at all wavelengths. It is given the name blackbody because an object that absorbs light at all wavelengths appears black to the human eye. By the end of the 19th century, several properties of blackbody radiation had been established. First, the total intensity I (the average rate of radiation of energy per unit surface area) emitted from a blackbody was shown to be proportional to the fourth power of its temperature: I=oT¹ This is called the Stefan-Boltzmann law for a blackbody. The constant of proportionality o is known as the Stefan-Boltzmann constant and was determined to be o = 5.67 x 10-8 W/(m². K¹). It had also been discovered that the wavelength at which the radiation intensity was maximum varied inversely with temperature. This result, known as the Wien displacement law, is written AmT = 2.90 x 10-³ m. K. where Am is the wavelength with the greatest radiated intensity. ✓…arrow_forwardAt what wavelength is the radiation emitted by the human body at its maximum? Assume a temperature of 37°C.arrow_forward
- The maximum intensity of radiation emitted by a star occurs at a surface temperature of 4.3 x 104 K. a) Calculate the wavelength of the emitted radiation when the intensity is maximum. b) Calculate the ratio of the intensity radiated at a wavelength of 60.0 nm to the maximum intensity. Assume that the star radiates like an ideal blackbody.arrow_forwardAssume the intensity of solar radiation incident on the cloud tops of the Earth is 1 677 W/m². (a) Taking the average Earth-Sun separation to be 1.496 x 10¹1 m, calculate the total power radiated by the Sun. 4.905E26 x Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. W (b) Determine the maximum value of the electric field in the sunlight at the Earth's location. kv/m (c) Determine the maximum value of the magnetic field in the sunlight at the Earth's location. μTarrow_forwardThe peak wavelength of radiation emitted by a black body at a temperature of 2000 K is 1.45 μm. If the peak wavelength of emitted radiation changes to 2.90 μm, then the temperature (in K) of the black body isarrow_forward
- You are working in a shop and are responsible for enacting the CoVID protocols before potential customers enter the shop (shoppers are not to be admitted if they have a temperature over 38.0°C). Unfortunately, the equipment you have been given to measure a person's temperature reports their peak wavelength instead. If a person has a peak wavelength of 9.320 μm, are they allowed to enter the store? A full solution must support your answer.arrow_forwardSuppose a star with radius 8.69 x 10° m has a peak wavelength of 684 nm in the spectrum of its emitted radiation. (a) Find the energy of a photon with this wavelength. 0.029e-17 J/photon (b) What is the surface temperature of the star? 4274.3 X K (c) At what rate is energy emitted from the star in the form of radiation? Assume the star is a blackbody (e = 1). 1.9934e17 Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. W (d) Using the answer to part (a), estimate the rate at which photons leave the surface of the star. X photons/sarrow_forwardSuppose a hot object radiates with the twice the intensity as the sun on earth, i.e. 2600W/m2. What is the energy density of this radiation?arrow_forward
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