The atoms in a nickel crystal vibrate as harmonic oscillators with an angular frequency of 2.3 × 10¹³rad/s. The mass of a nickel atom is 9.75 × 10^-26 kg. What is the difference in energy between adjacent vibrational energy levels of nickel? (h = 6.626 × 10^-34 J ∙ s, h = 1.055 × 10^-34 J ∙ s, 1 eV = 1.60 × 10^-19 J) A) 0.015 eV B) 0.019 eV C) 0.023 eV D) 0.027 eV E) 0.031 eV

Question

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The difference in energy between adjacent vibrational energy levels is given by:ΔE = hfwhere h is Planck's constant and f is the frequency of vibration.Plugging in the given values, we get:ΔE = (6.626 × 10^-34 J s)(2.3 × 10^13 rad/s) = 1.52 × 10^-20 JConverting to eV, we get:ΔE = (1.52 × 10^-20 J)/(1.60 × 10^-19 J/eV) = 0.015 eVTherefore, the correct answer is A.

The Atoms in a Nickel Crystal Vibrate as Harmonic Oscillators