Final answer:
The oscillation frequency of the HBr molecule with an energy difference between oscillator states of 0.330 eV is calculated using Planck's equation and the energy conversion from eV to joules, resulting in a frequency of approximately (7.97 x 10^13) Hz.
Step-by-step explanation:
The difference in energy between allowed oscillator states in HBr molecules is 0.330 eV. To find the oscillation frequency of the molecule, we can use the formula derived from Planck's equation, E = hf, where 'E' is the energy difference, 'h' is Planck's constant (6.626 x 10^-34 J s), and 'f' is the frequency. However, we first need to convert the energy from electron volts (eV) to joules (J), using the conversion factor 1 eV = 1.602 x 10^-19 J.
First, convert the energy difference to joules: 0.330 eV * 1.602 x 10^-19 J/eV = 5.286 x 10^-20 J.
Next, solve for frequency 'f': f = E/h = (5.286 x 10^-20 J) / (6.626 x 10^-34 J s) = 7.97 x 10^13 Hz.
Therefore, the correct answer, rounded to two decimal places, is (A) (7.97 x 10^13) Hz.