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	<title>The AstroStat Slog &#187; Kelvin</title>
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	<link>http://groundtruth.info/AstroStat/slog</link>
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		<title>keV vs keV [Eqn]</title>
		<link>http://groundtruth.info/AstroStat/slog/2008/eotw-kev-kev/</link>
		<comments>http://groundtruth.info/AstroStat/slog/2008/eotw-kev-kev/#comments</comments>
		<pubDate>Wed, 30 Jul 2008 17:00:20 +0000</pubDate>
		<dc:creator>vlk</dc:creator>
				<category><![CDATA[Astro]]></category>
		<category><![CDATA[High-Energy]]></category>
		<category><![CDATA[Jargon]]></category>
		<category><![CDATA[X-ray]]></category>
		<category><![CDATA[Angstrom]]></category>
		<category><![CDATA[Boltzmann]]></category>
		<category><![CDATA[EotW]]></category>
		<category><![CDATA[Equation]]></category>
		<category><![CDATA[Equation of the Week]]></category>
		<category><![CDATA[erg]]></category>
		<category><![CDATA[Kelvin]]></category>
		<category><![CDATA[keV]]></category>
		<category><![CDATA[Planck]]></category>
		<category><![CDATA[temperature]]></category>
		<category><![CDATA[units]]></category>
		<category><![CDATA[wavelength]]></category>

		<guid isPermaLink="false">http://groundtruth.info/AstroStat/slog/?p=360</guid>
		<description><![CDATA[I have noticed that our statistician collaborators are often confused by our units.  (Not a surprise; I, too, am constantly confused by our units.)  One of the biggest culprits is the unit of energy, [keV],  which is 1000 electron Volts, for the energy acquired by an electron when it falls through an [...]]]></description>
			<content:encoded><![CDATA[<p>I have noticed that our statistician collaborators are often confused by our units.  (Not a surprise; I, too, am constantly confused by our units.)  One of the biggest culprits is the unit of energy, [keV], <span id="more-360"></span> which is 1000 electron Volts, for the energy acquired by an electron when it falls through an electric potential of 1 Volt:</p>
<blockquote><p><strong>1 [eV] &#8801; 1.6021892 &#183; 10<sup>-19</sup> [Joule] &#8801; 1.6021892 &#183; 10<sup>-12</sup> [erg]</strong> .</p></blockquote>
<p>The confusion is because the same units are used to denote two separate quantities which happen to have similar magnitudes for a commonly encountered spectral model, Bremsstrahlung emission.</p>
<ol>
<li> the frequency &#957;, or wavelength &#955;, of a photon: As Planck discovered, the energy of a photon is directly related to the frequency &#957;,<br />
<blockquote><p><strong> E = h &#183; &#957; &#8801; h &#183; c / &#955; </strong> ,</p></blockquote>
<p>where h=6.6261760 &#183; 10<sup>-27</sup> [erg s] is <a href="http://en.wikipedia.org/wiki/Planck's_constant">Planck&#8217;s constant</a> and c=2.9979246 &#183; 10<sup>10</sup> [cm s<sup>-1</sup>] is the speed of light in vaccum.  When &#955; is given in [&Aring;ngstr&ouml;m] &#8801; 10<sup>-8</sup> [cm], we can convert it as</p>
<blockquote><p><strong> [keV] = 12.398521 / [&Aring;] </strong> ,</p></blockquote>
<p>which is an extraordinarily useful thing to know in high-energy astrophysics.</li>
<li> the temperature <em>T</em> of a gas or plasma: Here we look to thermodynamics, which relates the kinetic energy of random motion of particles in a gas to a gross property, the temperature of the gas,<br />
<blockquote><p><strong> E = k<sub>B</sub> &#183; T </strong> ,</p></blockquote>
<p>where k<sub>B</sub> = 1.3806620 &#183; 10<sup>-16</sup> [erg K<sup>-1</sup>] is <a href="http://en.wikipedia.org/wiki/Boltzmann_constant">Boltzmann&#8217;s constant</a>.  Then, a temperature in degrees Kelvin can be written in units of keV by converting it with the formula</p>
<blockquote><p><strong> [keV] = 8.6173468 &#183; 10<sup>-8</sup> &#183; [K] &#8801; 0.086173468 &#183; [MK] </strong> .</p></blockquote>
</li>
</ol>
<p>It is tempting to put the two together and interpret a temperature as a photon energy.  This is possible for the aforementioned Bremsstrahlung radiation, where plasma at a temperature <em>T</em> produces a spectrum of photons distributed as <em>e<sup>-h &#957; / k<sub>B</sub> T</sup></em> and it is possible to tie the temperature to the photon energy at the point where the numerator and denominator have the same numerical value.  For example, a 1 keV (temperature) Bremsstrahlung spectrum extends out to 1 keV (photon energy).  X-ray Astronomers use this as shorthand all the time, and it confuses the hell out of everybody else.</p>
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