9 In later chapters, we will see that the translational energy for a monoatomic

Question

9 In later chapters, we will see that the translational energy for a monoatomic ideal gas is -nRT. What is the average energy of a single gas atom (in Joules) at 300 K? [Hints: use the appropriate value of R for calculation of energy in terms of Joules; you can assume any value for n, the number of moles, you need to get from energy per mole to energy per atom.] Using your answer from the previous question, calculate the typical value of the translational energy quantum number n for a xenon atom in a 1 dm3 cube. Because a = b = c, nx-ny-nz-ntypical. Your answer should be a pretty big number. Comment on the magnitude of the energy level spacing between quantum states for this particle. Is it large or smal? In other words, how much do you expect the particle energy to change by changing the value of one of the translational quantum numbers by 1? 10. 11. 1-10 (once you know the equation to use, this is pretty much plug and chug. If you have difficulty getting started, it might help to draw an energy diagram.) 1-8 (Hint: what is the value of n when the electron is infinitely far from the nucleus?) 1-12 12. 13. 14.

Explanation / Answer

9. The formula you have to use is

3/2 * n * R * T, where

n is moles

R is gas constant

T is temperature in kelvin

in this case the proper value for R is R = 8.314 J / K mol

we are going to assume 1 mole so the energy will be:

3/2 * 1mol * 8.314 J / mol K * 300 K = 3741 Joules

this is the energy for 1 mole

now we have to use the avogadros number that says that 1 mole of something has

1 mole = 6.022x 1023 atoms

we only need to divide the enery for a mole by avogadros number so:

3741 Joules / 6.022x 1023 = 6.21 x 10-21 Joules / atom

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