The oxygen molecule (O2)may be regarded as two massesconnected by a spring. In v

Question

The oxygen molecule (O2)may be regarded as two massesconnected by a spring. In vibrational motion, each oxygen atomalternately approaches, then moves away from the center of mass ofthe system. If each oxygen atom of mass m=2.67 x 10-26 kg has avibrational energy of 1.6 x 10-21J and the effective springconstant is 50 N/m, then what is the amplitude of oscillation ofeach oxygen atom? The oxygen molecule (O2)may be regarded as two massesconnected by a spring. In vibrational motion, each oxygen atomalternately approaches, then moves away from the center of mass ofthe system. If each oxygen atom of mass m=2.67 x 10-26 kg has avibrational energy of 1.6 x 10-21J and the effective springconstant is 50 N/m, then what is the amplitude of oscillation ofeach oxygen atom?

Explanation / Answer

total energy = (1/2) k A2 . 1.6 x 10-21 = (1/2) * 50 *A2 . A =   8.00 x 10-12 m . Since each atom oscillates the same, the amplitude of eachis    4.00 x 10-12 m    (i.e. half the totalamplitude) . A =   8.00 x 10-12 m . Since each atom oscillates the same, the amplitude of eachis    4.00 x 10-12 m    (i.e. half the totalamplitude)

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