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

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Homework Help Overview

The discussion revolves around the vibrational motion of atoms in solids, specifically focusing on calculating the period of oscillation and the maximum speed of an atom based on given parameters such as amplitude and frequency.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants explore the relationship between frequency and period, with one participant attempting to apply the formula for speed but encountering difficulties. Another participant suggests using the concept of angular frequency and its relation to amplitude to find maximum speed.

Discussion Status

Some participants have provided guidance on the relationships between angular frequency, amplitude, and maximum speed. There is an ongoing exploration of calculations, with one participant expressing confusion about their results, while another indicates they have resolved their issue.

Contextual Notes

Participants are working within the constraints of a homework assignment, which may limit the information available and the methods they can use. There is a focus on understanding the underlying physics concepts rather than simply obtaining answers.

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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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