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Quantum Chemistry/Example 16
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Write an example question showing the calculation of the frequency of EM radiation emitted when a HCl molecule transitions from the J=1–>0 rotational state.
Example 16: Giving the bond length re=1.27Å, find the frequency of the EM radiation emitted when a HCl molecule transitions from the J=1→0 rotational state
Given the reduced mass (μ) and inertia (I), the energy can be found and subsequently be used to find frequency of the transition.
Note that for rotational states for J=1→0, ΔE is not required as the transition states are in the ground state.
Inertia can be found by using reduced mass of the molecule and their bond length(re = 1.27Å):
where reduced mass can be calculated by the following:
, where and
Convert to SI units:
, thus
Note that the bond length must also be in SI units,
1Å= 1×10-10m
Bond length = 1.27×10-10m
Inertia can now be calculated:
After calculating the inertia, energy can be found:
and , where h is the Planck's constant.
Frequency of the transmission can therefore be found: