In other problems and examples in the textbook we found theeffective spring stiffness corresponding to the interatomic forcefor aluminum and lead. Let's assume for the moment that, veryroughly, other atoms have similar values.
(a) What is the (very) approximate frequency f for theoscillation (\"vibration\") of H2, a hydrogen moleculecontaining two hydrogen atoms? Remember that frequency is definedas the number of complete cycles per second or \"hertz\": f= 1/T. There is no one correct answer, since we're justtrying to calculate the frequency approximately. However, justbecause we're looking for an approximate result doesn't mean thatall answers are correct! Calculations that are wildly indisagreement with what physics would predict for this situationwill be counted wrong.
f = Â Â ??? cycles/s (hertz)
(b) What is the (very) approximate frequency f for thevibration of O2, an oxygen molecule containing twooxygen atoms?
f = ?????? Â Â cycles/s (hertz)
(c) What is the approximate vibration frequency f ofD2, a molecule both of whose atoms are deuterium atoms(that is, each nucleus has one proton and one neutron)?
f = Â Â ????? cycles/s (hertz)
(d) Which of the following statements are true? (Select all thatapply.)
The estimated frequency for O2 is quite accuratebecause the mass of an oxygen atom is similar to the mass of analuminum atom. The true vibration frequency for D2 islower than the true vibration frequency for H2, becausethe mass is larger but the effective \"spring\" stiffness is nearlythe same, since it is related to the electronic structure, which isnearly the same for D2 and H2. The estimatedfrequencies for D2 and H2 are both quiteaccurate, because these are simple molecules, and the effectivespring stiffness is expected to be the same as we found inside ablock of metal. Neither of the estimated frequencies forD2 and H2 is accurate, but the ratio of theD2 frequency to the H2 frequency is quiteaccurate, because the \"spring\" represents the interatomic force,which is nearly the same for atoms with similar chemical structure(number of electrons).
