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towards an analysis of errors made by university students ... - DSpace

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y.E.N.<br />

DA C. ANDRADE)<br />

(Part one)<br />

Now, before the qu<strong>an</strong>tum theory was put<br />

forward,<br />

there was no notion <strong>of</strong> natural units <strong>of</strong> radi<strong>an</strong>t energy: it was<br />

believed that we could have <strong>an</strong>y amount <strong>of</strong> energy, as small<br />

as<br />

we pleased, radiated <strong>by</strong> a hot body or a luminous atom.<br />

It could<br />

however, be shown mathematically that, if this were true, we<br />

should expect a hot body to radiate nearly all its energy in<br />

the violet <strong>an</strong>d ultra-violet end <strong>of</strong> the spectrum, which we know<br />

to be against the facts <strong>of</strong><br />

observation.<br />

The problem was solved<br />

in the first year <strong>of</strong> the<br />

-present century, when Pl<strong>an</strong>ck showed that, to get the right<br />

result, it was necessary to make a revolutionary<br />

hypothesis:<br />

to suppose that radi<strong>an</strong>t energy was sent out in packets, as it<br />

were - in units or atoms <strong>of</strong> energy, just as matter existed<br />

in<br />

atomic units. We c<strong>an</strong>not have less th<strong>an</strong> <strong>an</strong> atom <strong>of</strong> lead,<br />

say;<br />

<strong>an</strong>y minute piece <strong>of</strong> lead must consist <strong>of</strong> a whole number <strong>of</strong><br />

atoms. We c<strong>an</strong>not have <strong>an</strong> electric charge <strong>of</strong> less th<strong>an</strong> <strong>an</strong><br />

electron.<br />

In the same way, we c<strong>an</strong>not have less th<strong>an</strong> z unit - or<br />

qu<strong>an</strong>tum,<br />

as it is called - <strong>of</strong> radi<strong>an</strong>t energy, <strong>an</strong>d <strong>an</strong>y body that sends<br />

out<br />

or absorbs radiation must deal with one qu<strong>an</strong>tum or a whole number<br />

<strong>of</strong><br />

qu<strong>an</strong>ta.<br />

The little parcel <strong>of</strong> light <strong>of</strong> one particular<br />

frequency in which radi<strong>an</strong>t energy is delivered is sometimes<br />

called a 'light dart', a very expressive term, but it is more<br />

generally known as a photon. The photon is simply a qu<strong>an</strong>tum <strong>of</strong><br />

radi<strong>an</strong>t energy, the only object <strong>of</strong> sometimes using the new<br />

term

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