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Problem 3 Easy Difficulty

Lightning produces a maximum air temperature on the order of $10^{4} \mathrm{K}$ , whereas a nuclear explosion produces a temperature on the order of $10^{7} \mathrm{K}$ . ( a) Use Wien's displacement law to find the order of magnitude of the wavelength of the thermally produced photons radiated with greatest
intensity by each of these sources. (b) Name the part of the electromagnetic spectrum where you would expect each to radiate most strongly.

Answer

a) $10^{-7} \mathrm{m} $ for lightning; $10^{-10} \mathrm{m}$ for nuclear explosion.
b) The lightning emits the radiation in ultraviolet range.
Nuclear explosion emits the radiation in the $x$ - ray range.

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Top Physics 103 Educators
Christina K.

Rutgers, The State University of New Jersey

Marshall S.

University of Washington

Zachary M.

Hope College

Jared E.

University of Winnipeg

Video Transcript

this exercise, we have the order of magnitudes of the temperature of lightning which is sent to the fourth Calvin and the order of magnitude of the temperature of a nuclear explosion, which is tend to the sound of Calvi. And in the first, on the first question, we have to calculate what is the order of magnitude off the wavelength at which the radiation is emitted with the maximum intensity that is from the max. And we know that according to beans, lol um, the Max times T equals 2.9 times 10 to the minus three meters. Calvin. So for the lightning, we have that Linda Max equals 2.9 times 10 to the minus three, divided by sen to the fourth Calvin. And this is of the order of magnitude off 10 to the minus seven meters. And for the nuclear explosion, we have London max equals 2.9 times 10 to the minus three, divided by 10 to them seventh. So this is a V border off 10 to the minus 10 meters in question. Be way. Are asked to classify thes wavelengths. Uh, came in visible light ultraviolent lie infrared x ray were asked just basically whereas to say in what part of the electromagnetic spectrum these wavelengths saw. And for the lightning, 10 to the minus seven is within the ultraviolet range. Okay, because Dutra violet like goes from about 10 centimeters to 400 meters. And here we have something about ah, 108 meters. And for the nuclear explosion, we we have radiation in the X ray ring because the X ray grain X ray range goes from 10 to the minus three millimeters to 10 millimeters. And here we have a wavelength of the order of 0.1 centimeters. Okay, so this concludes our exercise.

Universidade de Sao Paulo
Top Physics 103 Educators
Christina K.

Rutgers, The State University of New Jersey

Marshall S.

University of Washington

Zachary M.

Hope College

Jared E.

University of Winnipeg