- #1

catkin

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**[SOLVED] SHM: atom in a lattice**

## Homework Statement

From Advanced Physics by Adams and Allday. Spread 3.34, Q 5.

An atom of mass [tex]5 \times 10^{-26}[/tex] kg is in a cubic lattice with all bonds between adjacent pairs of atoms having a spring constant about 100 N/m. Estimate the natural frequency of oscillation of the atom. If it is able to absorb radiation at this frequency, what part of the electromagnetic spectrum does it absorb?

## Homework Equations

[tex]F = ma[/tex] (Newton 2)

[tex]F = -kx[/tex] (Hooke)

[tex]a = -\omega^{2}x[/tex] (SHM)

## The Attempt at a Solution

From Newton 2 and Hooke

[tex]a = -kx / m[/tex]

Substituting in SHM

[tex]-kx / m = -\omega^{2}x[/tex]

[tex]\omega = \sqrt{k/m}[/tex]

[tex]= \sqrt{\frac {100} {5 \times 10^{-26}}}[/tex]

[tex]= 4 \times 10^{13}[/tex] Hz ct1sf

My difficulty is that the answer given in the book is [tex]7.12 \times 10^{12}[/tex] Hz. What have I done wrong? Using [tex]\omega = \sqrt{k/m}[/tex] and the given value of m, k would have to be ~2.55 N/m. ?