Physics for Scientists and Engineers, Vol. 1
Physics for Scientists and Engineers, Vol. 1
6th Edition
ISBN: 9781429201322
Author: Paul A. Tipler, Gene Mosca
Publisher: Macmillan Higher Education
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Chapter 35, Problem 4P
To determine

The value of force constant for entire spring.

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Atoms vibrate relative to one another in molecules with the bond acting as a spring. Consider the H – CI bond, where the heavy Cl atom forms a stationary anchor for the very light H atom. That is, only the H atom moves, vibrating as a simple harmonic oscillator. (a) Give the equation that describes the allowed vibrational energy levels of the bond. (b) The force constant kf for the H – Cl bond is 516.3 N m'1. Given the mass of H equal to 1.7 x 1027 kg, determine the difference in energy (separation) between adjacent energy levels. (c) Calculate the zero-point energy of this molecular oscillator.
What is the minimum energy required to go from one vibrational state to the next higher vibrational state for a molecule whose vibrations are modeled by a harmonic oscillator?
Consider an isolated carbon atom being held in its equilibrium lattice site position by the mutual interaction with the neighboring atoms. If the spring constant driving the carbon atom back into its equilibrium lattice site is 21.71 N/m, what is the frequency of oscillation? The atomic mass of carbon is given in the periodic table. Give your answers in units of 1012 rad/s with 2 digits precision, rounding off to two decimal places, i.e. the nearest hundredths. (time budget 6min)
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