CMB Wavelength

Classical Mechanics Level 2

The cosmic microwave background CMB is a bath of blackbody radiation permeating the universe at a temperature of $2.7 \text{ K}$ . What is the wavelength of the radiation in the CMB in centimeters?

0.004

0.107

0.254

1.23

1 solution

Matt DeCross
May 15, 2016

Relevant wiki: Blackbody Radiation

The solution uses Wien's displacement law for blackbody radiation:

$\lambda = \frac{b}{T},$

where $\lambda$ is the wavelength, $T$ the temperature, and $b = 2.9 \times 10^{-3} \text{ m}\cdot \text{K}$ is Wien's constant. Plugging in $T = 2.7 \text{ K}$ obtains the answer.

I'm not a fan of the phrasing "permeating the universe at a temperature of...". Radiation doesn't have a temperature, and it seems like suggesting that it does could lead to big misconceptions. Is this accepted shorthand for "as if emitted by a black body of temperature..."?

Andrew Normand - 4 years, 3 months ago

Hi @Andrew Normand -- It's standard in cosmology to refer to the "temperature of the CMB" as the effective black-body temperature giving the peak of the observed frequency spectrum. In any case I would say this depends on your precise definition of temperature - two black bodies can come to thermal equilibrium through their shared radiation, suggesting that at least in some sense you can think of the radiation of each black body as part of a thermal reservoir at the black body temp. in contact with the other black body. I haven't seen any huge misconceptions that follow as a result of this identification, though perhaps some do exist.

Matt DeCross - 4 years, 3 months ago

@Matt DeCross Yes, having looked around a bit more it seems like it is common to apply the term temperature to isotropic back body radiation, and it fits a thermal equilibrium, zeroth law definition, so I take back my criticism. I'm a teacher, so worry about kids thinking that photons can have temperature, etc.

Andrew Normand - 4 years, 3 months ago

I'm pretty amazed at how this simple law has such varying applications...It's really cool, to be honest! :P

A Former Brilliant Member - 5 years, 1 month ago

Exactly. That's the power of Physics!

Swapnil Das - 5 years ago

CMB Wavelength

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