The ozone molecule O3 has a permanent dipole moment of 1.8×1030 Cm. Although the

Question

The ozone molecule O3 has a permanent dipole moment of 1.8×1030 Cm. Although the molecule is very slightly bent-which is why it has a dipole moment-it can be modeled as a uniform rod of length 2.5×1010 m with the dipole moment perpendicular to the axis of the rod. Suppose an ozone molecule is in a 8000 N/C uniform electric field. In equilibrium, the dipole moment is aligned with the electric field. But if the molecule is rotated by a small angle and released, it will oscillate back and forth in simple harmonic motion.

What is the frequency f of oscillation?

Explanation / Answer

frequency of oscillation is f = (1/2*pi)*sqrt(pE/I)

I is the moment of Inertia of the molecule = (1/12)*M*L^2

M is the mass of the each ozone molecule = 3*15.9994*1.67*10^-27= 8.01*10^-26 kg

then I = (1/12)*8.01*10^-26*(2.5*10^-10)^2 = 4.18*10^-46 Kg-m^2

Given that p = 1.8*10^-30 Cm

E = 8000 N/C

then

f = (1/2*pi)*sqrt(pE/I) = (1/(2*3.142))*sqrt(1.8*10^-30*8000/(4.18*10^-46))

f = 9.34*10^8 Hz

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