WEBVTT

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This is College Physics Answers
with Shaun Dychko.

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The peak intensity of the cosmic microwave
background radiation

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occurs at a wavelength of 1.1 millimeters

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and we are asked to figure out
the energy of that photon.

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So we have Planck's constant
times speed of light

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divided by the wavelength is the energy

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and <i>hc</i> can be written as

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1240 electron volt nanometers,

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which means we have to convert

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the length of this photon—this wavelength—
into nanometers

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so we multiply 1.1 nanometers
by 10 to the 6

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or 1.1 millimeters by 10 to the 6
nanometers per millimeter,

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this works out to 1.1 times 10 to
the minus 3 electron volts.

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Part (b) says there are approximately

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10 to the 9 photons for every particle
that has rest mass.

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So what is the total energy of
all the photons

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representative of a massive particle.

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So there's 10 to the 9 photons per particle

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times 1.1 times 10 to the minus 3
electron volts per photon

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and we get 1 megaelectron volt

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of photon energy for every particle.

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And the energy of a single
representative particle

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is half the energy of a proton

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and that's about 5 times 10 to
the 2 megaelectron volts

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and the question in part (d) is asking

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is space matter dominated or not?

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And the answer is yes, it is because

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there are 500 megaelectron volts of energy

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accounted for among massive particles

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for every 1 megaelectron volt
accounted for

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with photon energy.