In other problems and examples in the textbook we found the effective spring sti

Question

In other problems and examples in the textbook we found the effective spring stiffness corresponding to the interatomic force for aluminum and lead. Let's assume for the moment that, very roughly, other atoms have similar values (a) What is the (very) approximate frequency ffor the oscillation ("vibration") of H2, a hydrogen molecule containing two hydrogen atoms? Remember that frequency is defined as the number of complete cycles per second or "hertz": f = 1/T There is no one correct answer, since we're just trying to calculate the frequency approximately. However, just because we're looking for an approximate result doesn't mean that all answers are correct! Calculations that are wildly in disagreement with what physics would predict for this situation will be counted wrong cycles/s (hertz) (b) What is the (very) approximate frequency f for the vibration of O2, an oxygen molecule containing two oxygen atoms? cycles/s (hertz) (c) What is the approximate vibration frequency fof D2, a molecule both of whose atoms are deuterium atoms (that is, each nucleus has one proton and one neutron)? cycles/s (hertz) (d) Which of the following statements are true? (Select all that apply.) O The true vibration frequency for D2 is lower than the true vibration frequency for H2, because the mass is larger but the effective "spring" stiffness is nearly the same, since it is related to the electronic structure, which is nearly the same for D2 and H The estimated frequencies for D2 and H2 are both quite accurate, because these are simple molecules, and the effective spring stiffness is expected to be the same as we found inside a block of metal O The estimated frequency for 02 is quite accurate because the mass of an oxygen atom is similar to the m ass of an aluminum atom. ONeither of the estimated frequencies for D2 and H2 is accurate, but the ratio of the D2 frequency to the H2 frequencyis quite accurate, because the "spring" represents the interatomic force, which is nearly the same for atoms with similar chemical structure (number of electrons)

Explanation / Answer

This problem is a standard problem. The aluminium has a fixed spring stiffness values, so does mass of Hydorgen, oxygen and deuterium atom

We can use the following formula

w=sqrt(k/m) where k is spring stiffness and m is mass of atom.

So they have a standard frequency values

f(H2) = 1.4e13

f(O2) = 3.5e12

f(D2) = 1e13

As we can see frequency of D2 is lower can frequency of H2, Option 1 is correct and option 4 are correct, the ratio of frequency is same for atoms with similar chemical structure.

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