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<p>So the eigenvalues for the particle in a box are</p>
<p><br>
</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><msub><mi>E</mi><mi>n</mi></msub><mo>=</mo><mfrac><mrow><msup><mi>n</mi><mn>2</mn></msup><msup><mi>h</mi><mn>2</mn></msup></mrow><mrow><mn>8</mn><mi>m</mi><msup><mi>L</mi><mn>2</mn></msup></mrow></mfrac></mrow><annotation
encoding="TeX">E_n=\frac{n^2 h^2}{8 m L^2} </annotation></semantics></math><br>
</p>
For the 1D particle in a box problem from the worksheet we needed
the LUMO and HOMO transition energy. The LUMO (n=6) to the HOMO
(n=5) transition energy is given by the difference of these two
energy levels... <br>
<p><br>
</p>
<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>E</mi><mn>6</mn></msub><mo>−</mo><msub><mi>E</mi><mn>5</mn></msub><mo>=</mo><mfrac><mrow><msup><mn>6</mn><mn>2</mn></msup><msup><mi>h</mi><mn>2</mn></msup></mrow><mrow><mn>8</mn><mi>m</mi><msup><mi>L</mi><mn>2</mn></msup></mrow></mfrac><mo>−</mo><mfrac><mrow><msup><mn>5</mn><mn>2</mn></msup><msup><mi>h</mi><mn>2</mn></msup></mrow><mrow><mn>8</mn><mi>m</mi><msup><mi>L</mi><mn>2</mn></msup></mrow></mfrac><mo>=</mo><mo
stretchy="false">(</mo><msup><mn>6</mn><mn>2</mn></msup><mo>−</mo><msup><mn>5</mn><mn>2</mn></msup><mo
stretchy="false">)</mo><mfrac><msup><mi>h</mi><mn>2</mn></msup><mrow><mn>8</mn><mi>m</mi><msup><mi>L</mi><mn>2</mn></msup></mrow></mfrac></mrow><annotation
encoding="TeX">E_6-E_5=\frac{6^2h^2}{8mL^2}-\frac{5^2
h^2}{8mL^2}=(6^2-5^2)\frac{h^2}{8mL^2}
</annotation></semantics></math><br>
</p>
<div class="moz-cite-prefix">On 12/1/23 00:01, wrote:<br>
</div>
<blockquote type="cite"
cite="mid:e7a500c0c28c4ffabf3f684366ba8df6@SA1PR01MB6528.prod.exchangelabs.com">
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<div dir="ltr">On number 1 of the worksheet we solved from LUMO
to HOMO and our n value was 6^2-5^2. If we are asked to solve
from HOMO to LUMO would we then plug in 5^2 -6^2 or would it
just be the higher number minus the lower?</div>
<div dir="ltr"><br>
</div>
<div dir="ltr">Thank you,</div>
<div dir="ltr"><br>
</div>
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<div class="moz-signature">-- <br>
<b><em>Andrew J. Pounds, Ph.D.</em></b><br>
<em>Professor of Chemistry and Computer Science</em><br>
<em>Director of the Computational Science Program</em><br>
<em>Mercer University</em><br>
<em>1501 Mercer University Drive, Macon, GA 31207 </em><br>
<em>(478) 301-5627</em><br>
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