All books

Professional

Apps About Coach Log in Start reading

Chemistry · Glossary

What is Thermal wavelength?

Definition 10.10 University Chemistry — Year 3 · Chapter 10 — Statistical Thermodynamics: Partition Functions

The thermal wavelength of a molecule of mass mm at temperature TT is Λ=h2πmkT\Lambda = \dfrac{h}{\sqrt{2\pi mkT}}.

Examples

Example 10.12 (Argon in a flask)

For argon (M=39.95 g/molM = 39.95\,\mathrm{g}/\mathrm{mol}) at 298.15 K298.15\,\mathrm{K}, Λ=16.0 pm\Lambda = 16.0\,\mathrm{pm}, a tenth of an atomic diameter. In 1 dm31\,\mathrm{dm}^{3}, qT=10−3/(1.600×10−11)3=2.44×1029q^{\mathrm T} = 10^{-3}/(1.600\times10^{-11})^3 = 2.44 \times 10^{29} translational states are thermally accessible, far more than the 2.4×10222.4\times10^{22} atoms the flask holds at 1 bar1\,\mathrm{bar}: each state is almost always empty, the condition under which the molecules can be counted as below.

Read in context →