Question

Atoms in a solid are not stationary, but vibrate about their equilibrium positions. Typically, the frequency of vibration is about f = 4.11 x 1012 Hz, and the amplitude is about 1.23 x 10^-11 m. For a typical atom, what is its (a) maximum speed and (b) maximum acceleration

Answer 1

To develop this problem it is necessary to use the equations of description of the simple harmonic movement in which the acceleration and angular velocity are expressed as a function of the Amplitude.

Our values are given as

$f = 4.11 *10^{12} Hz$

$A = 1.23 * 10^{-11}m$

The angular velocity of a body can be described as a function of frequency as

$\omega = 2\pi f$

$\omega = 2\pi 4.11 *10^{12}$

$\omega=2.582*10^{13} rad/s$

PART A) The expression for the maximum angular velocity is given by the amplitude so that

$V = A\omega$

$V =( 1.23 * 10^{-11})(2.582*10^{13})$

$V = = 317.586m/s$

PART B) The maximum acceleration on your part would be given by the expression

$a = A \omega^2$

$a =( 1.23 * 10^{-11})(2.582*10^{13})^2$

$a= 8.2*10^{15}m/s^2$