Pure Microwave absorptions at 84.421, 90.449, and 96.477 GHz on flowing dibromine gas over hot copper...
Pure Microwave absorptions at 84.421, 90.449, and 96.477 GHz on flowing dibromine gas over hot copper metal at 1100 K. What transitions do these frequencies represent? What is the bond length of the species formed? Assume a linear rotor.
Homework Answers
96.477 - 90.449 = 6.028 and 90.449 - 84.421 = 6.028
So, constant difference of 6.028 GHz or 6.028 ×109
s-1.
ΔE = 2h2/8π2I
So,
84.421 / 6.028 = 14 ie. J = 13 → J = 14
90.449 / 6.028 = 15 ie. J = 14 → J = 15
96.477 / 6.028 = 16 ie. J = 15 → J = 16
ΔE = 2h2/8π2I = hv = h (6.028 ×109 s-1)
I = 2 h/(8π2
6.028×109s-1)
I = 2 (6.626×10-34 J.s)/(8π2
6.028×109s-1)
I = 2.784×10-45 kg m2
But, I = μr2
μ = (0.063×0.079)/(0.063+0.079)NA =
5.82×10-26 kg
r = √(I/μ) = 218.6×10-12 m = 218.6 pm
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