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	<title>MrReid.org</title>
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	<link>http://wordpress.mrreid.org</link>
	<description>... the blog of Mr Reid, physics teacher</description>
	<lastBuildDate>Sat, 04 Feb 2012 17:00:45 +0000</lastBuildDate>
	<language>en</language>
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		<title>Whiteboards</title>
		<link>http://wordpress.mrreid.org/2012/02/04/whiteboards/</link>
		<comments>http://wordpress.mrreid.org/2012/02/04/whiteboards/#comments</comments>
		<pubDate>Sat, 04 Feb 2012 17:00:45 +0000</pubDate>
		<dc:creator>Mr Reid</dc:creator>
				<category><![CDATA[General]]></category>
		<category><![CDATA[teaching]]></category>
		<category><![CDATA[whiteboard]]></category>

		<guid isPermaLink="false">http://wordpress.mrreid.org/?p=4462</guid>
		<description><![CDATA[Sometimes after a lesson I take a photograph of the whiteboard left over. Some recent photographs are below.]]></description>
			<content:encoded><![CDATA[<p>Sometimes after a lesson I take a photograph of the whiteboard left over. Some recent photographs are below.</p>
<p><img class="alignnone size-full wp-image-4466" title="blackboard1" src="http://wordpress.mrreid.org/wp-content/uploads/2012/02/blackboard1.jpg" alt="" width="640" height="383" /></p>
<p><img class="alignnone size-full wp-image-4467" title="blackboard2" src="http://wordpress.mrreid.org/wp-content/uploads/2012/02/blackboard2.jpg" alt="" width="640" height="383" /></p>
<p><img class="alignnone size-full wp-image-4468" title="blackboard3" src="http://wordpress.mrreid.org/wp-content/uploads/2012/02/blackboard3.jpg" alt="" width="640" height="383" /></p>
<p><img class="alignnone size-full wp-image-4469" title="blackboard4" src="http://wordpress.mrreid.org/wp-content/uploads/2012/02/blackboard4.jpg" alt="" width="640" height="383" /></p>
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		<title>The cost of coins</title>
		<link>http://wordpress.mrreid.org/2012/01/23/the-cost-of-coins/</link>
		<comments>http://wordpress.mrreid.org/2012/01/23/the-cost-of-coins/#comments</comments>
		<pubDate>Mon, 23 Jan 2012 11:00:27 +0000</pubDate>
		<dc:creator>Mr Reid</dc:creator>
				<category><![CDATA[General]]></category>
		<category><![CDATA[coins]]></category>
		<category><![CDATA[currency]]></category>
		<category><![CDATA[metal]]></category>
		<category><![CDATA[money]]></category>

		<guid isPermaLink="false">http://wordpress.mrreid.org/?p=4405</guid>
		<description><![CDATA[It used to be the case that coins used as currency had value because of the material from which they were made: a solid gold coin weighing one ounce had the same value as one ounce of gold. The introduction of &#8230; <a href="http://wordpress.mrreid.org/2012/01/23/the-cost-of-coins/">Continue reading <span class="meta-nav">&#8594;</span></a>]]></description>
			<content:encoded><![CDATA[<p>It used to be the case that coins used as currency had value because of the material from which they were made: a solid gold coin weighing one ounce had the same value as one ounce of gold. The introduction of fiat currencies, issued by central banks, that only have value because a government decrees by law that they do, allowed governments to move away from this dependence on rare metals.</p>
<p><img class="noborder size-full wp-image-4419 aligncenter" title="uk-coins" src="http://wordpress.mrreid.org/wp-content/uploads/2012/01/uk-coins.jpg" alt="" width="640" height="315" /></p>
<p>UK coins come in four “flavours”: the “copper” 1p and 2p coins, the “silver” 5p, 10p, 20p and 50p coins and the larger and heavier £1 and two-tone £2 coins. Before 1992 the “copper” 1p and 2p coins really did contain copper, being made from a bronze containing 97% copper, 2.5% zinc and 0.5% tin. With a mass of 3.56 and 7.12 grams respectively the pre-1992 coins contained 3.54 and 6.91 grams of copper; at the current bulk price and the current USD-GBP exchange rate this makes a <a title="Current value of 1p coin as scrap copper" href="http://www.wolframalpha.com/input/?i=3.54+grams+of+copper+in+pence">1p coin worth 1.66 pence</a> and a <a title="Current value of 2p coin as scrap" href="http://www.wolframalpha.com/input/?i=6.94+grams+of+copper+in+pence">2p coin worth 3.23 pence</a> (those links will take you to automatically calculated values using current values for spot price and exchange rate).</p>
<p><a href="http://wordpress.mrreid.org/wp-content/uploads/2012/01/copper-price-graph.png"><img class="size-large wp-image-4418 aligncenter" title="copper-price-graph" src="http://wordpress.mrreid.org/wp-content/uploads/2012/01/copper-price-graph-640x331.png" alt="" width="640" height="331" /></a>If you were able to buy pre-1992 1p and 2p coins in bulk for their face value you could make a profit by melting them down and selling the resulting copper as scrap (though this is <a title="Relevant section of 1971 act" href="http://www.legislation.gov.uk/ukpga/1971/24/section/10">illegal under the 1971 Coinage Act</a>). This increasing price of copper in the early lead to a change from bronze to copper-plated steel and this makes it very easy to differentiate between the old and new 1p/2p coins: pre-1992 coins are not magnetic and post-1992 coins are.</p>
<p>The “silver” coins have previously been made from cupro-nickel, an alloy of copper and nickel in a 75:25 ratio. In terms of its raw metal, a 3.25 gram five pence coin, containing <a title="Current value of metals in 5p coin" href="http://www.wolframalpha.com/input/?i=%282.44+grams+of+copper+in+pence%29+%2B+%280.81+grams+of+nickel+in+pence%29">2.44 grams of copper and 0.81 grams of nickel</a> is currently worth 3.08 pence (1.14p for the copper and 1.94p for the nickel). A 6½ gram ten pence coin is <a title="Current value of 10p coin" href="http://www.wolframalpha.com/input/?i=%28%280.75*6.5%29+grams+of+copper+in+pence%29+%2B+%28%280.25*6.5%29+grams+of+nickel+in+pence%29">worth 6.16p</a>, a five gram twenty pence coin is <a title="Current value of 20p coin" href="http://www.wolframalpha.com/input/?i=%28%280.75*5%29+grams+of+copper+in+pence%29+%2B+%28%280.25*5%29+grams+of+nickel+in+pence%29">worth 4.74p</a> and an eight gram fifty pence coin is <a title="Current value of 50p coin" href="http://www.wolframalpha.com/input/?i=%28%280.75*8%29+grams+of+copper+in+pence%29+%2B+%28%280.25*8%29+grams+of+nickel+in+pence%29">worth 7.58p</a>.</p>
<p>From January 2012 the “silver” coins will be made from nickel-plated steel (making them magnetic), a change driven probably by the rising cost of both copper and nickel. (In May 2007, when the price of nickel was at a peak, a five pence coin was worth more than six pence as scrap copper and nickel).</p>
<p><a href="http://wordpress.mrreid.org/wp-content/uploads/2012/01/copper-nickel-price-graph.png"><img class="size-large wp-image-4417 aligncenter" title="copper-nickel-price-graph" src="http://wordpress.mrreid.org/wp-content/uploads/2012/01/copper-nickel-price-graph-640x331.png" alt="" width="640" height="331" /></a>The high value of the £1 coin <small>(<a title="Value of £1 coin" href="http://www.wolframalpha.com/input/?i=%28%280.70*9.5%29+grams+of+copper+in+pence%29+%2B+%28%280.245*9.5%29+grams+of+zinc+in+pence%29+%2B+%28%280.055*9.5%29+grams+of+nickel+in+pence%29">current value</a>)</small>, composed of 70% copper, 24.5% zinc, and 5.5% nickel and the £2 coin, with a cupro-nickel core surrounded by a ring of 76% copper, 20% zinc, and 4% nickel, makes them unlikely to ever approach a situation in which they are worth more than their face value.</p>
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		<title>Technetium-99m generators</title>
		<link>http://wordpress.mrreid.org/2012/01/15/technetium-99m-generators/</link>
		<comments>http://wordpress.mrreid.org/2012/01/15/technetium-99m-generators/#comments</comments>
		<pubDate>Sun, 15 Jan 2012 11:00:29 +0000</pubDate>
		<dc:creator>Mr Reid</dc:creator>
				<category><![CDATA[General]]></category>
		<category><![CDATA[medicine]]></category>
		<category><![CDATA[nuclear]]></category>

		<guid isPermaLink="false">http://wordpress.mrreid.org/?p=4375</guid>
		<description><![CDATA[Technetium-99m is a radioactive tracer that is used in twenty million medical diagnostic procedures per year. At least 31 radiopharmaceuticals based on Tc-99m are used for imaging and studying organs such as the brain, heart muscle, thyroid, lungs, liver, gallbladder &#8230; <a href="http://wordpress.mrreid.org/2012/01/15/technetium-99m-generators/">Continue reading <span class="meta-nav">&#8594;</span></a>]]></description>
			<content:encoded><![CDATA[<p><a title="Tc-99m information" href="http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/technetium.html">Technetium-99m</a> is a radioactive tracer that is used in twenty million medical diagnostic procedures per year. At least 31 <a title="What are radiopharmaceuticals?" href="http://www.wisegeek.com/what-are-radiopharmaceuticals.htm">radiopharmaceuticals</a> based on Tc-99m are used for imaging and studying organs such as the brain, heart muscle, thyroid, lungs, liver, gallbladder and kidneys, as well as the skeleton and blood and for the investigation of tumours.</p>
<p>The ‘m’ in the name of technetium-99m indicates that it is <em>metastable</em>. Tc-99m is radioactive because one or more of the protons and neutrons in its nucleus is in an excited state. Tc-99m decays into Tc-99 with a half-life of six hours and this makes it particularly well suited to use in the body: after one day (four half-lives) only 6.3% of the initial Tc-99m remains. (It’s worth noting that the non-metastable technetium-99 is also radioactive, but with a half-life of 211000 years, it presents a <a title="Long half lives aren't dangerous" href="http://wordpress.mrreid.org/2010/10/26/long-half-life-dangerous/">very low risk</a>.)</p>
<p>This short half-life also creates a problem: obtaining Tc-99m when required. Hospitals cannot run their own nuclear reactors and so they rely on <a title="More information on technetium generators" href="http://www.bnl.gov/bnlweb/history/tc-99m.asp">technetium generators</a> - machines that produce Tc-99m from the decay of its parent isotope molybdenum-99. Molybdenum-99 has a longer half-life (66 hours) and can therefore be transported to hospitals and still remain useful for up to a week.</p>
<p><img class="alignnone noborder size-full wp-image-4379" title="mo-99-to-tc-99" src="http://wordpress.mrreid.org/wp-content/uploads/2012/01/mo-99-to-tc-99.png" alt="" width="640" height="88" /></p>
<p>Molybdenum-99 is produced in nuclear reactors by bombarding a highly enriched uranium target with neutrons, causing it to <a title="Nuclear fission" href="http://hyperphysics.phy-astr.gsu.edu/hbase/nucene/fission.html">fission</a>, forming Mo-99 (and many other isotopes) as it does. The vast majority of Mo-99 is produced by five nuclear reactors around the world that are specifically devoted to the production of nuclear isotopes for medicine: <a title="NRU website" href="http://www.nrucanada.ca/en/home/insidenru/nruwhatdoesitdo.aspx">NRU</a> in Canada, <a title="BR2 website" href="http://www.sckcen.be/en/Our-Services/Irradiations/Radioisotope-production">BR2</a> in Belgium, SAFARI-1 in South Africa, HFR Petten in the Netherlands and OSIRIS-1 in France.* Temporary shutdowns of NRU and HFR Petten in the 2000s led to a long-term shortage of Mo-99.</p>
<p>Once Mo-99 has been produced it is placed into a technetium generator and these generators are transported to hospitals. The technetium generators make use of the fact that molybdenum likes to bond with aluminium oxide (alumina) but technetium does not. The generators are “milked” by drawing a saline solution across an inner molybdenum/alumina capsule; during this elution process any technetium that has formed will be drawn away with the saline and can then be used in tests.</p>
<p><img class="alignnone size-full wp-image-4381" title="technetium-generator" src="http://wordpress.mrreid.org/wp-content/uploads/2012/01/technetium-generator.jpg" alt="" width="640" height="980" /></p>
<p style="text-align: center;"><small>A cutaway model of a technetium generator.</small></p>
<p>The molybdenum/alumina sample is placed in the centre of the device, surrounded by shielding (painted red in this case). Saline is injected through one of the tubes at the top of the device and flows into a shielded container through the other tube, after having passed over the sample and “picked up” radioactive technetium-99m.</p>
<p><small>* Mo-99 is also produced in much smaller amounts from low-enriched uranium at the OPAL reactor in Australia and at other sites.</small></p>
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		<title>Plug wiring colour scheme</title>
		<link>http://wordpress.mrreid.org/2012/01/06/plug-wiring-colour-scheme/</link>
		<comments>http://wordpress.mrreid.org/2012/01/06/plug-wiring-colour-scheme/#comments</comments>
		<pubDate>Fri, 06 Jan 2012 11:00:18 +0000</pubDate>
		<dc:creator>Mr Reid</dc:creator>
				<category><![CDATA[General]]></category>
		<category><![CDATA[colour]]></category>
		<category><![CDATA[electricity]]></category>
		<category><![CDATA[plug]]></category>
		<category><![CDATA[safety]]></category>

		<guid isPermaLink="false">http://wordpress.mrreid.org/?p=4361</guid>
		<description><![CDATA[UK plugs use brown insulation for the live wire, blue insulation for the neutral wire and green with yellow stripes insulation for the earth wire. But why this particular combination of colours? The answer is deceptively simple: there is no &#8230; <a href="http://wordpress.mrreid.org/2012/01/06/plug-wiring-colour-scheme/">Continue reading <span class="meta-nav">&#8594;</span></a>]]></description>
			<content:encoded><![CDATA[<p>UK plugs use brown insulation for the live wire, blue insulation for the neutral wire and green with yellow stripes insulation for the earth wire.</p>
<p><img class="alignnone size-full wp-image-4364" title="plug-original" src="http://wordpress.mrreid.org/wp-content/uploads/2012/01/plug-original.jpg" alt="" width="640" height="640" /></p>
<p>But why this particular combination of colours? The answer is deceptively simple: there is no type of colour blindness that will result in these wires becoming confused.</p>
<p><img class="alignnone size-full wp-image-4363" title="plug-deuteranopia" src="http://wordpress.mrreid.org/wp-content/uploads/2012/01/plug-deuteranopia.jpg" alt="" width="640" height="640" /></p>
<p style="text-align: center;"><small>Above: how a UK plug looks to someone who is red-green colourblind.</small></p>
<p><img class="alignnone size-full wp-image-4365" title="plug-tritanopia" src="http://wordpress.mrreid.org/wp-content/uploads/2012/01/plug-tritanopia.jpg" alt="" width="640" height="640" /></p>
<p style="text-align: center;"><small>Above: how a UK plug looks to someone who is blue-yellow colourblind.</small></p>
<p>One of the lesser-known safety features of a UK plug is the extra distance that the neutral wire has to travel when compared to the live wire. If someone pulls on the mains cable the live wire will disconnect first, making the plug safer.</p>
<p>Under the <a title="IEC 60446 regulation" href="http://en.wikipedia.org/wiki/IEC_60446">IEC 60446</a> standard only black, brown, red, orange, yellow, green, blue, violet, grey, white, pink and turquoise are acceptable colours for labelling wires. Countries must choose an appropriate selection of colours that eliminates the possibility of confusion.</p>
<p><img class="alignnone size-full wp-image-4366" title="wire-colours" src="http://wordpress.mrreid.org/wp-content/uploads/2012/01/wire-colours.jpg" alt="" width="640" height="160" /></p>
<p style="text-align: center;"><small>IEC 60446 colours. From top to bottom: normal vision, deuteranopic vision, tritanopic vision.</small></p>
<p><span id="more-4361"></span></p>
<p>During the course of writing this post I realised that there are no copyright-free high-resolution photographs of the inside of a UK plug available online. I hereby release the image below into the public domain.</p>
<p style="text-align: center;"><a href="http://wordpress.mrreid.org/wp-content/uploads/2012/01/plug-original-large.jpg"><img class="size-thumbnail wp-image-4368 aligncenter" title="plug-original-large" src="http://wordpress.mrreid.org/wp-content/uploads/2012/01/plug-original-large-150x150.jpg" alt="" width="150" height="150" /></a><small>Click to enlarge.</small></p>
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		<title>Night vision</title>
		<link>http://wordpress.mrreid.org/2012/01/02/night-vision/</link>
		<comments>http://wordpress.mrreid.org/2012/01/02/night-vision/#comments</comments>
		<pubDate>Mon, 02 Jan 2012 11:00:23 +0000</pubDate>
		<dc:creator>Mr Reid</dc:creator>
				<category><![CDATA[General]]></category>
		<category><![CDATA[eye]]></category>
		<category><![CDATA[light]]></category>
		<category><![CDATA[vision]]></category>

		<guid isPermaLink="false">http://wordpress.mrreid.org/?p=4326</guid>
		<description><![CDATA[The vision of human beings is well-adapted to daylight; the human eye has evolved to see in the range of wavelengths that are brightest in the spectrum of light that the Sun emits. The intensity of the light the Sun &#8230; <a href="http://wordpress.mrreid.org/2012/01/02/night-vision/">Continue reading <span class="meta-nav">&#8594;</span></a>]]></description>
			<content:encoded><![CDATA[<p>The vision of human beings is well-adapted to daylight; the human eye has evolved to see in the range of wavelengths that are brightest in the spectrum of light that the Sun emits.</p>
<p style="text-align: center;"><a href="http://wordpress.mrreid.org/wp-content/uploads/2012/01/solar-emission-wavelength.jpg"><img class="size-large wp-image-4339 aligncenter" title="solar-emission-wavelength" src="http://wordpress.mrreid.org/wp-content/uploads/2012/01/solar-emission-wavelength-640x331.jpg" alt="" width="640" height="331" /></a><small>The intensity of the light the Sun emits by wavelength, with the visible region highlighted.</small></p>
<p>But humans don’t see particularly well in the dark. The <a title="What are cone cells?" href="http://simple.wikipedia.org/wiki/Cone_cell">cones</a> that are responsible for colour vision don’t function well at low light intensities, which is why night vision is almost entirely monochromatic — in the dark humans see in black and white.</p>
<p>When moving from bright light into darkness the first thing that happens to the eye is that the pupil dilates to allow in more light. The <a title="More information on the iris" href="http://www.tedmontgomery.com/the_eye/iris.html">iris dilator muscle</a> causes the pupil to increase in diameter by a factor of five (from 2 mm to 10 mm), increasing the amount of light entering the eye by about twenty-five (5<sup>2</sup>) times, but this isn’t enough for true night vision.</p>
<p><img class="size-full wp-image-4340 aligncenter" title="pupil-dilating-reverse" src="http://wordpress.mrreid.org/wp-content/uploads/2012/01/pupil-dilating-reverse.gif" alt="" width="640" height="366" /></p>
<p>The chemical <a title="More information on rhodopsin" href="http://www.chm.bris.ac.uk/webprojects2003/rogers/998/Rhoeye.htm">rhodopsin</a> that is present in the rod (brightness-sensing) cells is responsible for night vision. When exposed to light, rhodopsin immediately (within 200 femtoseconds*) splits to form a chemical called photorhodopsin, and then soon afterwards (within a few picoseconds) another chemical called bathorhodopsin.</p>
<p>The splitting of rhodopsin is accompanied by the formation of other chemicals called <a title="More information on retinal" href="http://www.ch.ic.ac.uk/vchemlib/mim/bristol/retinal/retinal_text.htm">retinals</a>, and during this splitting process a signal is sent down the optic nerve to the brain, registering the detection of light. (Retinal is created from vitamin A, and so people with a diet lacking in vitamin A frequently suffer from <a title="More information on night blindness" href="http://www.medterms.com/script/main/art.asp?articlekey=6448">night blindness</a>.)</p>
<p><img class="noborder size-full wp-image-4332 aligncenter" title="rhodopsin-lipid" src="http://wordpress.mrreid.org/wp-content/uploads/2011/12/rhodopsin-lipid.jpg" alt="" width="640" height="329" /></p>
<p style="text-align: center;"><small>A molecule of rhodopsin (rainbow-coloured) embedded in a lipid bilayer.<br />
A (black) retinal molecule is bound within the rhodopsin.</small></p>
<p>Over time, and at a consistent rate, the opsins and retinals recombine to form rhodopsin. If the eye is exposed to bright light all the rhodopsin splits at once (a process called photobleaching). When subsequently exposed to darkness there is therefore no rhodopsin to split and the eye cannot detect light properly. The person in question must wait for the rhodopsin to naturally recombine over time before proper vision can return, a process that takes between ten and thirty minutes to occur. When fully accustomed to the dark, the eye is between ten thousand and a million times more sensitive to light than previously.</p>
<p>The rhodopsin in human eyes is less-sensitive to red light than to other colours and therefore night vision is not particularly effected by red light. This is why red light is used in darkrooms and in aircraft before night-time parachute jumps.</p>
<p><img class="size-full wp-image-4331 aligncenter" title="airdrop-red-light" src="http://wordpress.mrreid.org/wp-content/uploads/2011/12/airdrop-red-light.jpg" alt="" width="640" height="426" /></p>
<p>Human eyes, unlike the eyes of many animals, do not have the <a title="What is the tapetum lucidum?" href="http://en.wikipedia.org/wiki/Tapetum_lucidum"><em>tapetum lucidum</em></a> which gives those animals superior night vision. The <em>tapetum lucidum</em> sits behind the retina and acts like a mirror, reflecting back photons of light that were not initially absorbed by the retina, giving the retina a “second chance” to detect the light. This improves their night vision and is what gives rise to the phenomenon of “eyeshine” often seen when taking photographs of animals.</p>
<p><img class="size-full wp-image-4333 aligncenter" title="tapetum-lucidum" src="http://wordpress.mrreid.org/wp-content/uploads/2011/12/tapetum-lucidum.jpg" alt="" width="640" height="401" /></p>
<p style="text-align: center;"><small>The <em>tapetum lucidum</em> seen in a dissected calf’s eye.</small></p>
<p><img class="size-full wp-image-4334 aligncenter" title="eyeshine-raccoon" src="http://wordpress.mrreid.org/wp-content/uploads/2011/12/eyeshine-raccoon.jpg" alt="" width="640" height="345" /></p>
<p style="text-align: center;"><small>“Eyeshine” is very obvious in this photograph of a raccoon.</small></p>
<p><small>* Interestingly, the splitting of rhodopsin into photorhodopsin and retinal seems to be the fastest chemical reaction that has been directly studied.</small></p>
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		<title>The most radioactive parts of the UK</title>
		<link>http://wordpress.mrreid.org/2011/12/28/radiation-in-the-uk/</link>
		<comments>http://wordpress.mrreid.org/2011/12/28/radiation-in-the-uk/#comments</comments>
		<pubDate>Wed, 28 Dec 2011 11:00:11 +0000</pubDate>
		<dc:creator>Mr Reid</dc:creator>
				<category><![CDATA[General]]></category>
		<category><![CDATA[radioactivity]]></category>
		<category><![CDATA[radon]]></category>

		<guid isPermaLink="false">http://wordpress.mrreid.org/?p=4301</guid>
		<description><![CDATA[The average radioactive background dose in the UK is 2.7 millisieverts. Of this 2.7 mSv, 1.35 mSv comes from radioactive radon gas leaking out of the ground. This radioactive radon (Rn-222) is produced by the decay of uranium-238, after a series &#8230; <a href="http://wordpress.mrreid.org/2011/12/28/radiation-in-the-uk/">Continue reading <span class="meta-nav">&#8594;</span></a>]]></description>
			<content:encoded><![CDATA[<p>The average radioactive background dose in the UK is 2.7 millisieverts. Of this 2.7 mSv, 1.35 mSv comes from radioactive radon gas leaking out of the ground.</p>
<p><img class="noborder alignnone size-full wp-image-4308" title="radon-graph" src="http://wordpress.mrreid.org/wp-content/uploads/2011/12/radon-graph.png" alt="" width="640" height="130" /></p>
<p>This radioactive radon (Rn-222) is produced by the decay of uranium-238, after a series of intermediate non-gas stages that cannot escape from rocks.</p>
<p><img class="noborder alignnone size-full wp-image-4310" title="radon-decay-chain" src="http://wordpress.mrreid.org/wp-content/uploads/2011/12/radon-decay-chain.png" alt="" width="640" height="34" /></p>
<p>Because radon has such a large effect on the annual radiation dose that someone receives, it is closely monitored. In the UK, this monitoring is done by the <a title="HPA radon website" href="http://www.hpa.org.uk/Topics/Radiation/UnderstandingRadiation/UnderstandingRadiationTopics/Radon/">Health Protection Agency</a> (HPA). One of the things that the HPA does it produce radon maps, showing which areas of the UK have the highest presence of radon.</p>
<p><img class="alignnone size-full wp-image-4311" title="uk-radon" src="http://wordpress.mrreid.org/wp-content/uploads/2011/12/uk-radon.jpg" alt="" width="640" height="794" /></p>
<p>The map is graded by the percentage of homes in that area which have a level of radon beyond the action level of <a title="What is 200 Bq/m3" href="http://www.wolframalpha.com/input/?i=200+Bq%2Fm^3">200 becquerels per cubic metre</a> (200 radon decays per second per cubic metre).</p>
<p>There are a number of important radon hotspots in the UK. The most noticeable one is Cornwall in the south-west where the average UK background dose is 7.8 mSv, nearly three times the national average. This is due to the presence of igneous granite, which naturally contains more uranium (10–20 parts per million) than other rocks.</p>
<p>Radioactive areas tend to be hilly, where igneous rocks have been forced to the surface or left behind by the erosion of softer sedimentary rocks (the Chiltern Hills are particularly radioactive, for example). The Yorkshire Dales sit on top of an underground deposit of pink granite called the <a title="What is Wensleydale Granite" href="www.google.co.uk/search?q=Wensleydale+Granite">Wensleydale Granite</a> that lies underneath the <a title="More information on Askrigg Block" href="http://www.yorkshire-dales.com/askrigg-block.html">Askrigg Block</a>, and the Peak District features many granite outcroppings.</p>
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		<title>Biosphere lungs</title>
		<link>http://wordpress.mrreid.org/2011/12/27/biosphere-lungs/</link>
		<comments>http://wordpress.mrreid.org/2011/12/27/biosphere-lungs/#comments</comments>
		<pubDate>Tue, 27 Dec 2011 11:00:54 +0000</pubDate>
		<dc:creator>Mr Reid</dc:creator>
				<category><![CDATA[General]]></category>
		<category><![CDATA[biosphere]]></category>
		<category><![CDATA[pressure]]></category>

		<guid isPermaLink="false">http://wordpress.mrreid.org/?p=4197</guid>
		<description><![CDATA[Some people refer to the rainforests as “Earth’s lungs”. In reality this is quite far from the truth, as rainforests actually contribute little (net) oxygen to Earth’s atmosphere; 70% of oxygen production is done by water-bourne green algae and the &#8230; <a href="http://wordpress.mrreid.org/2011/12/27/biosphere-lungs/">Continue reading <span class="meta-nav">&#8594;</span></a>]]></description>
			<content:encoded><![CDATA[<p>Some people refer to the rainforests as “Earth’s lungs”. In reality this is quite far from the truth, as rainforests actually contribute little (net) oxygen to Earth’s atmosphere; 70% of oxygen production is done by water-bourne <a title="What is green algae?" href="http://www.ucmp.berkeley.edu/greenalgae/greenalgae.html">green algae</a> and the <a title="What are cyanobacteria?" href="http://www.ucmp.berkeley.edu/bacteria/cyanointro.html">cyanobacteria</a> present in every habitat on Earth.</p>
<p><a title="Biosphere 2 wikipedia page" href="http://en.wikipedia.org/wiki/Biosphere_2">Biosphere 2</a>, a sealed ecological system built in Arizona to study the interaction between different forms of life and as a test of the possibility of using closed systems in space colonisation, also had lungs.</p>
<p><iframe src="http://maps.google.co.uk/maps?q=32.578778,-110.850594&amp;oe=utf-8&amp;client=firefox-a&amp;ie=UTF8&amp;hq=&amp;gl=uk&amp;ll=32.577797,-110.849375&amp;spn=0.016906,0.018539&amp;t=h&amp;z=16&amp;vpsrc=6&amp;output=embed" frameborder="0" marginwidth="0" marginheight="0" scrolling="no" width="640" height="640"></iframe></p>
<p>Biosphere 2’s oxygen came from the facility’s six biomes: a 1900 square meter rainforest, an 850 square meter “ocean”, a 450 square meter mangrove wetland, a 1300 square meter savannah grassland, a 1400 square meter <a title="What is a fog desert?" href="http://en.wikipedia.org/wiki/Fog_desert">fog desert</a> and a 2500 square meter agricultural system.</p>
<p><img class="alignnone size-full wp-image-4296" title="biosphere-interior" src="http://wordpress.mrreid.org/wp-content/uploads/2011/12/biosphere-interior.jpg" alt="" width="640" height="480" /></p>
<p>During the day the heat of the Arizona sun would cause the air inside the facility to expand. In order to avoid the large pressure difference that this would create (5000 Pa, or 5% of standard atmospheric pressure), Biosphere 2’s creators included two giant hemispherical “lungs”.</p>
<p><img class="alignnone size-full wp-image-4288" title="biosphere-lung-exterior" src="http://wordpress.mrreid.org/wp-content/uploads/2011/12/biosphere-lung-exterior.jpg" alt="" width="640" height="398" /></p>
<p>As the air inside the facility expanded it would flow through underground tunnels into the lungs. Each lung contained a large weight hanging from a rubber sheet; as the air expanded during the day the increased pressure would raise the weight into the air. In the evening, as the air cooled, the weight would pull the rubber sheet back down and push air back into the facility, thereby equalising any pressure difference as it appeared.</p>
<p><img class="alignnone size-full wp-image-4294" title="biosphere-lung-interior" src="http://wordpress.mrreid.org/wp-content/uploads/2011/12/biosphere-lung-interior.jpg" alt="" width="640" height="359" /></p>
<p style="text-align: right;"><small>Source: <a title="Source" href="http://www.flickr.com/photos/sminor/4098882118/sizes/l/in/photostream/">lumierefl</a></small></p>
<p><small>William Dempster, “Biosphere 2 engineering design”, <em>Ecological Engineering</em> 13 (1999): 31–42 doi:<a title="DOI link" href="http://dx.doi.org/10.1016/S0925-8574(98)00090-1">10.1016/S0925-8574(98)00090–1</a> (<a title="Link to PDF of paper" href="http://amazonpire.info/PDF/workshop0309/research/Dempster.pdf">.PDF</a>).</small></p>
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		<title>Anscombe’s quartet</title>
		<link>http://wordpress.mrreid.org/2011/12/21/anscombes-quartet/</link>
		<comments>http://wordpress.mrreid.org/2011/12/21/anscombes-quartet/#comments</comments>
		<pubDate>Wed, 21 Dec 2011 11:00:53 +0000</pubDate>
		<dc:creator>Mr Reid</dc:creator>
				<category><![CDATA[General]]></category>
		<category><![CDATA[graphs]]></category>
		<category><![CDATA[mathematics]]></category>

		<guid isPermaLink="false">http://wordpress.mrreid.org/?p=4192</guid>
		<description><![CDATA[Anscombe’s quartet is four sets of data that are used to demonstrate the importance of graphing data. Set 1 Set 2 Set 3 Set 4 x y x y x y x y 10 8.04 10 9.14 10 7.46 8 &#8230; <a href="http://wordpress.mrreid.org/2011/12/21/anscombes-quartet/">Continue reading <span class="meta-nav">&#8594;</span></a>]]></description>
			<content:encoded><![CDATA[<p>Anscombe’s quartet is four sets of data that are used to demonstrate the importance of graphing data.</p>
<table>
<tbody>
<tr>
<td></td>
<td style="text-align: center;" colspan="2"><strong>Set 1</strong></td>
<td style="text-align: center;" colspan="2"><strong>Set 2</strong></td>
<td style="text-align: center;" colspan="2"><strong>Set 3</strong></td>
<td style="text-align: center;" colspan="2"><strong>Set 4</strong></td>
</tr>
<tr>
<td width="10%"></td>
<td style="text-align: center;" width="11.25%"><em>x</em></td>
<td style="text-align: center;" width="11.25%"><em>y</em></td>
<td style="text-align: center;" width="11.25%"><em>x</em></td>
<td style="text-align: center;" width="11.25%"><em>y</em></td>
<td style="text-align: center;" width="11.25%"><em>x</em></td>
<td style="text-align: center;" width="11.25%"><em>y</em></td>
<td style="text-align: center;" width="11.25%"><em>x</em></td>
<td style="text-align: center;" width="11.25%"><em>y</em></td>
</tr>
<tr>
<td></td>
<td style="text-align: center;">10</td>
<td style="text-align: center;">8.04</td>
<td style="text-align: center;">10</td>
<td style="text-align: center;">9.14</td>
<td style="text-align: center;">10</td>
<td style="text-align: center;">7.46</td>
<td style="text-align: center;">8</td>
<td style="text-align: center;">6.58</td>
</tr>
<tr>
<td></td>
<td style="text-align: center;">8</td>
<td style="text-align: center;">6.95</td>
<td style="text-align: center;">8</td>
<td style="text-align: center;">8.14</td>
<td style="text-align: center;">8</td>
<td style="text-align: center;">6.77</td>
<td style="text-align: center;">8</td>
<td style="text-align: center;">5.76</td>
</tr>
<tr>
<td></td>
<td style="text-align: center;">13</td>
<td style="text-align: center;">7.58</td>
<td style="text-align: center;">13</td>
<td style="text-align: center;">8.74</td>
<td style="text-align: center;">13</td>
<td style="text-align: center;">12.7</td>
<td style="text-align: center;">8</td>
<td style="text-align: center;">7.71</td>
</tr>
<tr>
<td></td>
<td style="text-align: center;">9</td>
<td style="text-align: center;">8.81</td>
<td style="text-align: center;">8</td>
<td style="text-align: center;">8.87</td>
<td style="text-align: center;">9</td>
<td style="text-align: center;">7.11</td>
<td style="text-align: center;">8</td>
<td style="text-align: center;">8.84</td>
</tr>
<tr>
<td></td>
<td style="text-align: center;">11</td>
<td style="text-align: center;">8.33</td>
<td style="text-align: center;">11</td>
<td style="text-align: center;">9.26</td>
<td style="text-align: center;">11</td>
<td style="text-align: center;">7.81</td>
<td style="text-align: center;">8</td>
<td style="text-align: center;">8.74</td>
</tr>
<tr>
<td></td>
<td style="text-align: center;">14</td>
<td style="text-align: center;">9.96</td>
<td style="text-align: center;">14</td>
<td style="text-align: center;">8.10</td>
<td style="text-align: center;">14</td>
<td style="text-align: center;">8.84</td>
<td style="text-align: center;">8</td>
<td style="text-align: center;">7.04</td>
</tr>
<tr>
<td></td>
<td style="text-align: center;">6</td>
<td style="text-align: center;">7.24</td>
<td style="text-align: center;">6</td>
<td style="text-align: center;">6.13</td>
<td style="text-align: center;">6</td>
<td style="text-align: center;">6.08</td>
<td style="text-align: center;">8</td>
<td style="text-align: center;">5.25</td>
</tr>
<tr>
<td></td>
<td style="text-align: center;">4</td>
<td style="text-align: center;">4.26</td>
<td style="text-align: center;">4</td>
<td style="text-align: center;">3.10</td>
<td style="text-align: center;">4</td>
<td style="text-align: center;">5.39</td>
<td style="text-align: center;">19</td>
<td style="text-align: center;">12.5</td>
</tr>
<tr>
<td></td>
<td style="text-align: center;">12</td>
<td style="text-align: center;">10.8</td>
<td style="text-align: center;">12</td>
<td style="text-align: center;">9.13</td>
<td style="text-align: center;">12</td>
<td style="text-align: center;">8.15</td>
<td style="text-align: center;">8</td>
<td style="text-align: center;">5.56</td>
</tr>
<tr>
<td></td>
<td style="text-align: center;">7</td>
<td style="text-align: center;">4.82</td>
<td style="text-align: center;">7</td>
<td style="text-align: center;">7.26</td>
<td style="text-align: center;">7</td>
<td style="text-align: center;">6.42</td>
<td style="text-align: center;">8</td>
<td style="text-align: center;">7.91</td>
</tr>
<tr>
<td></td>
<td style="text-align: center;">5</td>
<td style="text-align: center;">5.68</td>
<td style="text-align: center;">5</td>
<td style="text-align: center;">4.74</td>
<td style="text-align: center;">5</td>
<td style="text-align: center;">5.73</td>
<td style="text-align: center;">8</td>
<td style="text-align: center;">6.89</td>
</tr>
<tr style="border-top: 10px;">
<td style="text-align: center;">Mean</td>
<td style="text-align: center;">9</td>
<td style="text-align: center;">7.50</td>
<td style="text-align: center;">9</td>
<td style="text-align: center;">7.50</td>
<td style="text-align: center;">9</td>
<td style="text-align: center;">7.50</td>
<td style="text-align: center;">9</td>
<td style="text-align: center;">7.50</td>
</tr>
<tr>
<td style="text-align: center;">Variance</td>
<td style="text-align: center;">11</td>
<td style="text-align: center;">4.13</td>
<td style="text-align: center;">11</td>
<td style="text-align: center;">4.13</td>
<td style="text-align: center;">11</td>
<td style="text-align: center;">4.12</td>
<td style="text-align: center;">11</td>
<td style="text-align: center;">4.12</td>
</tr>
<tr>
<td style="text-align: center;">PMCC</td>
<td style="text-align: center;" colspan="2">0.82</td>
<td style="text-align: center;" colspan="2">0.82</td>
<td style="text-align: center;" colspan="2">0.82</td>
<td style="text-align: center;" colspan="2">0.82</td>
</tr>
</tbody>
</table>
<p>Each set of data has near-identical statistical properties: the same <a title="Definition of average" href="http://simple.wikipedia.org/wiki/Average">average</a> and <a title="What is variance?" href="http://simple.wikipedia.org/wiki/Variance">variance</a> (for both <em>x</em> and <em>y)</em>, and the same <a title="PMCC explanation" href="http://mathworld.wolfram.com/CorrelationCoefficient.html">product moment correlation coefficient</a> and <a title="Linear regression explanation" href="http://graphpad.com/curvefit/linear_regression.htm">linear regression</a> line. When plotted, however, they look entirely different. (The scale of the last graph is different from the others.)</p>
<p><a href="http://wordpress.mrreid.org/wp-content/uploads/2011/12/anscombe-set1.png"><img class="size-large wp-image-4272 aligncenter" title="anscombe-set1" src="http://wordpress.mrreid.org/wp-content/uploads/2011/12/anscombe-set1-640x331.png" alt="" width="640" height="331" /></a></p>
<p><a href="http://wordpress.mrreid.org/wp-content/uploads/2011/12/anscombe-set2.png"><img class="size-large wp-image-4273 aligncenter" title="anscombe-set2" src="http://wordpress.mrreid.org/wp-content/uploads/2011/12/anscombe-set2-640x331.png" alt="" width="640" height="331" /></a></p>
<p><a href="http://wordpress.mrreid.org/wp-content/uploads/2011/12/anscombe-set3.png"><img class="size-large wp-image-4274 aligncenter" title="anscombe-set3" src="http://wordpress.mrreid.org/wp-content/uploads/2011/12/anscombe-set3-640x331.png" alt="" width="640" height="331" /></a></p>
<p><a href="http://wordpress.mrreid.org/wp-content/uploads/2011/12/anscombe-set4.png"><img class="size-large wp-image-4275 aligncenter" title="anscombe-set4" src="http://wordpress.mrreid.org/wp-content/uploads/2011/12/anscombe-set4-640x331.png" alt="" width="640" height="331" /></a></p>
<p>You can download Anscombe’s quartet as an <a href="http://wordpress.mrreid.org/wp-content/uploads/2011/12/anscombes-quartet.xls">Excel spreadsheet</a>.</p>
<p><small>Francis Anscombe, “Graphs in Statistical Analysis”, <em>American Statistician</em> 27(1) (1973): 17‑21. <a title="Link to journal site" href="http://www.jstor.org/stable/2682899">http://www.jstor.org/stable/2682899</a> (<a title="Link to copy of paper" href="http://www.sjsu.edu/faculty/gerstman/StatPrimer/anscombe1973.pdf">.PDF</a>).</small></p>
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		<title>Haversine formula</title>
		<link>http://wordpress.mrreid.org/2011/12/20/haversine-formula/</link>
		<comments>http://wordpress.mrreid.org/2011/12/20/haversine-formula/#comments</comments>
		<pubDate>Tue, 20 Dec 2011 11:00:55 +0000</pubDate>
		<dc:creator>Mr Reid</dc:creator>
				<category><![CDATA[General]]></category>
		<category><![CDATA[earth]]></category>
		<category><![CDATA[mathematics]]></category>

		<guid isPermaLink="false">http://wordpress.mrreid.org/?p=4089</guid>
		<description><![CDATA[The haversine formula is used to calculate the distance between two points on the Earth’s surface specified in longitude and latitude. d is the distance between two points with longitude and latitude (ψ,φ) and r is the radius of the &#8230; <a href="http://wordpress.mrreid.org/2011/12/20/haversine-formula/">Continue reading <span class="meta-nav">&#8594;</span></a>]]></description>
			<content:encoded><![CDATA[<p>The haversine formula is used to calculate the distance between two points on the Earth’s surface specified in longitude and latitude.</p>
<p><img class="noborder aligncenter size-full wp-image-4228" title="haversine" src="http://wordpress.mrreid.org/wp-content/uploads/2011/12/haversine.png" alt="" width="639" height="72" /></p>
<p><em>d</em> is the distance between two points with longitude and latitude (ψ,φ) and <em>r</em> is the radius of the Earth.</p>
<p>As an example I have calculated the distance between Fermilab in Illinois (<a title="Map link" href="http://toolserver.org/~geohack/geohack.php?pagename=Fermilab&amp;params=41_49_55_N_88_15_26_W_region:US-IL_type:landmark">41° 49′ 55″ N, 88° 15′ 26″ W</a>) and CERN’s Meyrin campus in Switzerland (<a title="Map link" href="http://toolserver.org/~geohack/geohack.php?pagename=CERN&amp;params=46_14_03_N_6_03_10_E_region:CH_type:landmark">46° 14′ 3″ N, 6° 3′ 10″ E</a>). There’s a little too much maths for this site to handle so I have included a .PDF file of the working below.</p>
<p><a href="http://wordpress.mrreid.org/wp-content/uploads/2011/12/haversine.pdf"><img class="size-full wp-image-4229 aligncenter" title="haversine-paper" src="http://wordpress.mrreid.org/wp-content/uploads/2011/12/haversine-paper.jpg" alt="" width="640" height="913" /></a></p>
<p>The value calculated is 7084 km, which isn’t quite correct. This is because the formula assumes that the Earth is a perfect sphere when in fact it is an oblate spheroid. To compensate for this <a title="Vincenty's Formulae" href="http://en.wikipedia.org/wiki/Vincenty%27s_formulae">Vincenty’s Formulae</a> must be used; these are much more complicated but give a more accurate value of 7103 km.</p>
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		<title>Patterns in birthdays</title>
		<link>http://wordpress.mrreid.org/2011/12/17/patterns-in-birthdays/</link>
		<comments>http://wordpress.mrreid.org/2011/12/17/patterns-in-birthdays/#comments</comments>
		<pubDate>Sat, 17 Dec 2011 11:00:40 +0000</pubDate>
		<dc:creator>Mr Reid</dc:creator>
				<category><![CDATA[General]]></category>
		<category><![CDATA[birth]]></category>
		<category><![CDATA[sex]]></category>

		<guid isPermaLink="false">http://wordpress.mrreid.org/?p=4180</guid>
		<description><![CDATA[If births were evenly distributed throughout the year (i.e. a 1 in 365 chance of being born on any given day) then the graph of number of births against birth month would look like the one below: You’re least likely &#8230; <a href="http://wordpress.mrreid.org/2011/12/17/patterns-in-birthdays/">Continue reading <span class="meta-nav">&#8594;</span></a>]]></description>
			<content:encoded><![CDATA[<p>If births were evenly distributed throughout the year (i.e. a 1 in 365 chance of being born on any given day) then the graph of number of births against birth month would look like the one below:</p>
<p><a href="http://wordpress.mrreid.org/wp-content/uploads/2011/12/birth-rate-expected.png"><img class="size-large wp-image-4182 aligncenter" title="birth-rate-expected" src="http://wordpress.mrreid.org/wp-content/uploads/2011/12/birth-rate-expected-640x331.png" alt="" width="640" height="331" /></a></p>
<p>You’re least likely to be born in February, because it only has 28 days, and then slightly more likely to be born in the 31-day months of January, March, May, July, August, October and December than in the 30-day months of April, June, September and November.</p>
<p>I took the data from nearly a thousand pupils and looked at how their dates of birth compared with the expected values. (Included with the data are error bars of one standard deviation.)</p>
<p><a href="http://wordpress.mrreid.org/wp-content/uploads/2011/12/birth-rate-comparison.png"><img class="size-large wp-image-4183 aligncenter" title="birth-rate-comparison" src="http://wordpress.mrreid.org/wp-content/uploads/2011/12/birth-rate-comparison-640x331.png" alt="" width="640" height="331" /></a></p>
<p>The results for April, September and December (particularly December) show birth rates above what would be expected if births are random, and the results for July and August show depressed birth rates.</p>
<p>Considering the months where births are more likely than they should be and working backwards we find the most likely “sex months” to be March, July and December. These seem fairly sensible as all of these months coincide with major holiday periods: Easter, the long Summer Holiday and Christmas/New Year. People are more likely to be “celebrating” and to have more free time during these periods, and March and December have <a title="How does day length change throughout the year" href="http://wordpress.mrreid.org/2010/10/31/why-change-the-clocks/">long, cold and dark nights</a> when people are more likely to stay indoors in the evening than go out.</p>
<p>The “sex months” for the lowest birth rates are more puzzling: October and November. I suspect that it has to do with <a title="SAD information" href="http://www.nhs.uk/conditions/Seasonal-affective-disorder/Pages/Introduction.aspx">Seasonal Affective Disorder</a> (SAD) and that the generalised depression that comes with SAD includes reduced sex drive; this is combated come December by the general presence of good cheer and plenty of alcohol to lower inhibitions. It is also possible that parents are deliberately choosing when to conceive in order to avoid their child being the youngest in the school year, something that <a title="Link to paper." href="http://www.biomedcentral.com/1471-2458/5/102">has been shown* to have a negative effect</a>.</p>
<p><strong>Update:</strong> Thanks to <a title="S3yM5n on Twitter" href="http://twitter.com/#!/S3yM5n">@S3ym5n</a> I’ve now included national data for 2010.</p>
<p><a href="http://wordpress.mrreid.org/wp-content/uploads/2011/12/national-birth-rate-data.png"><img class="size-large wp-image-4348 aligncenter" title="national-birth-rate-data" src="http://wordpress.mrreid.org/wp-content/uploads/2011/12/national-birth-rate-data-640x331.png" alt="" width="640" height="331" /></a>In the national data it is September and October that show birth rates above what is expected, making December and January the most popular sex months. April appears to be the only month with a significantly lower birth rate, making July, when people are out and about in the nice weather rather than stuck indoors, the least popular sex month.</p>
<p><span id="more-4180"></span></p>
<p>There is relatively little variation in birth rate from year to year:</p>
<p style="text-align: left;"><a href="http://wordpress.mrreid.org/wp-content/uploads/2011/12/ten-year-birth-rate.png"><img class="wp-image-4349 aligncenter alignnone" title="ten-year-birth-rate" src="http://wordpress.mrreid.org/wp-content/uploads/2011/12/ten-year-birth-rate-640x331.png" alt="" width="640" height="331" /></a></p>
<p style="text-align: left;"><small>* Lars Lien et al. “Is relatively young age within a school year a risk factor for mental health problems and poor school performance? A population-based cross-sectional study of adolescents in Oslo, Norway” <em>BMC Public Health</em> 5(102) (2005). doi: <a title="DOI link" href="http://dx.doi.org/10.1186/1471-2458-5-102">10.1186/1471–2458-5–102</a>.</small></p>
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