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Homework Help: Quantom of energy in Entropy

  1. Dec 3, 2008 #1
    The interatomic spring stiffness for magnesium is determined from Young's modulus measurements to be 12 N/m. The mass of one mole of magnesium is 0.012 kg. If we model a block of magnesium as a collection of atomic "oscillators" (masses on springs), what is one quantum of energy for one of these atomic oscillators? Note that since each oscillator is attached to two "springs", and each "spring" is half the length of the interatomic bond, the effective interatomic spring stiffness for one of these oscillators is 4 times the calculated value given above.

    Use these precise values for the constants:
    hbar= 1.054610e-34 J ยท s (Planck's constant divided by 2)
    Avogadro's number = 6.022110e23 molecules/mole
    k = 1.380710e-23 J/K (the Boltzmann constant)

    I tried that one quantum of energy would be hbar*sqrt(ks/m) = 1.054e-34*sqrt((4*12)/(.012/6.02e23)) which is incorrect. The 'hint' is that one quantum of energy is the amount of energy required to raise one atomic oscillator from one energy level to the next highest energy level
  2. jcsd
  3. Apr 23, 2009 #2
    That equation is exactly right, but make sure you are putting in at least 5 numbers for the answer just like the question asks.
  4. Apr 23, 2009 #3
    whenever I calculate the energy, I get an error on my calculator b/c it can't do 4.91e26 factorial. How did you input that as an answer?
  5. Apr 23, 2009 #4
    I can't get the right answer with that equation, too

    hbar*sqrt(ks/m) = 1.054e-34*sqrt((4*12)/(.012/6.02e23) = energy

    btw, Jchohnac, where does the "factorial" come from????
  6. Apr 23, 2009 #5
    i got the first question right with that equation, but i'm talking about the table and calculating the energy.
  7. Apr 23, 2009 #6
    For the energy all you need to do is multiply the energy of one quantum by the number of quantums.

    So if 5.17597e-21 was the energy of one quantum, multipl that by 20 and you get the enegery. For entropy, it is just k*ln(# of ways) given in the table
  8. Apr 23, 2009 #7
    hey, Jchohnac, how did u calculate out the energy of one quantum ??
    is it hbar*sqrt(ks/m)???
    or hbar*sqrt(4*ks/m)???
  9. Apr 23, 2009 #8
    1.054e-34*sqrt((4*12)/(.012/6.02e23))...i followed this with my numbers
  10. Apr 23, 2009 #9
    Does anyone know how to do the very last part on question 1?...

    There are 100 atoms in this object. What is the heat capacity on a per-atom basis? (Note that at high temperatures the heat capacity on a per-atom basis approaches the classical limit of 3k = 4.210-23 J/K/atom.)

    Heat capacity per atom = ?? J/K/atom
  11. Apr 23, 2009 #10
    never mind, i got it
  12. Dec 2, 2009 #11
    I still dun get the Heat Capacity per atom.. Can anyone help me? Thanks
  13. Dec 3, 2009 #12
    One Quantum/ delta Temp/ 100 atoms = Heat Capacity
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