Calculating Period and Speed of Atomic Vibrations | Atom Motion in Solids

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SUMMARY

The discussion focuses on calculating the period and maximum speed of atomic vibrations in solids, specifically at room temperature where the amplitude is approximately 10^-9 cm and the frequency is around 10^12 Hz. The period of oscillation is confirmed to be 10^-12 seconds, derived from the formula T = 1/f. To find the maximum speed of an atom, participants suggest using the relationship v = ωA, where ω is the angular frequency calculated as ω = 2πf.

PREREQUISITES
  • Understanding of simple harmonic motion (SHM)
  • Familiarity with the relationship between frequency and period
  • Knowledge of angular frequency and its calculation
  • Basic skills in algebra for solving equations
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  • Study the derivation of angular frequency in simple harmonic motion
  • Learn about the energy of particles in SHM and its implications
  • Explore the relationship between amplitude, frequency, and maximum speed in oscillatory motion
  • Investigate the effects of temperature on atomic vibrations in solids
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Students studying physics, particularly those focusing on solid-state physics and atomic behavior, as well as educators seeking to clarify concepts related to atomic vibrations and simple harmonic motion.

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Homework Statement


Atoms in a solid are in continuous vibrational motion due to thermal energy. At room temperature, the amplitude of these atomic bibrations is typically about 10^-9 cm, and their frequency is on the order of 10^12 Hz. What is the approximate period of oscillation of a typical atom? What is the mazimum speed of such an atom?


Homework Equations


(1/f)=T


The Attempt at a Solution


For period of oscillation i know the answer is 10^-12, but I do not know the formula for finding the speed of the atom. I used C=(lambda/f) but this didn't work. Any help would be appreciated. Thanks
 
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The energy of a particle in SHM is mv^2/2, where v is max speed and also kA^2/2, where A is amplitude. Do you know omega in terms of k and m? Then you can figure it out.
 
ok so omega = sqrt*k/m then multiply omega x A to get max speed? But i get a very small number and I know it's not correct, what am I doing wrong?
 
Last edited:
(omega = 2*pi*f = 2*pi/T.)

Probably doing some arithmetical errors. Show your calculations.
 
oh sweet, i got it thanks!
 

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