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On 12/14/2011 03:19 PM, Vanessa.Marie.Breslin wrote:
<blockquote
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<div style="direction: ltr; font-family: Tahoma; color: rgb(0, 0,
0); font-size: 10pt;">Dr. Pounds,
<div><br>
</div>
<div>On HW set 8 your problem #2, I had two questions. The
problem is: Calculate the fractional occupations (Ni/N) of the
energy levels of a particle in a 1-D box at a temperature at
which the population of the n=2 level is 0.421 of the
population of the n=1 level. The energy levels of the particle
in the 1-D box are nondegenerate. The relative energies of the
levels can simply be taken as 1, 4, 9, 16, 25,...</div>
<div><br>
</div>
<div>My first question is about a calculation. When trying to
find the temperature, I got ln(N2/N1)=-3/kT, where
(N2/N1)=0.421. So I calculated my temperature to be
2.511*10^23 Kelvin. Is that correct? Although that temperature
checks out with the other calculation steps later in the
problem, I was just curious because this does not seem like a
reasonable temperature to me. </div>
<div><br>
</div>
</div>
</blockquote>
You are really only looking for the "relative" temperature here --
so it would be relative to some other state that is not specified.
That being said, there is no need to calculate the actual
temperature in this problem -- as can keep "kT" together.<br>
<br>
ln(N<sub>2</sub>/N<sub>1</sub>) = -3 kT<br>
<br>
N<sub>2</sub>/N<sub>1</sub> = 0.421 (from the problem definition)<br>
<br>
kT = -3 / ln(N<sub>2</sub>/N<sub>1</sub>) <br>
<br>
kT = -3 / ln(.421)<br>
<br>
kT = 3.47 <br>
<br>
<br>
<br>
<blockquote
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</div>
<div>A second question I have about the same homework set
problem is when you calculated the molecular partition
function (q), how do you know when to stop adding energy
terms? Why did you stop at n=8?</div>
<div><br>
</div>
<div>Those are all the questions I have. </div>
<div><br>
</div>
<div>Thanks,</div>
<div>Vanessa</div>
</div>
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Lets calculate terms 1 and 8<br>
<br>
exp(-1/3.47) = 0.7497<br>
<br>
exp(-64/3.47) = 9.77e-9 <br>
<br>
My calculator has a 10 digit display. If I added any other terms
the value in the display didn't change...<br>
<br>
<br>
<br>
The fraction in the first level is 0.651<br>
<br>
The fraction in the second level is 0.274<br>
<br>
The fraction in the third level is 0.0649<br>
<br>
The fraction in the fourth level is 0.0086<br>
<br>
The fraction in the fifth level is 0.0006<br>
<br>
<br>
<pre class="moz-signature" cols="72">--
Andrew J. Pounds, Ph.D. (<a class="moz-txt-link-abbreviated" href="mailto:pounds@theochem.mercer.edu">pounds@theochem.mercer.edu</a>)
Associate Professor of Chemistry and Computer Science
Mercer University, Macon, GA 31207 (478) 301-5627
</pre>
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