What Frequency Does an Atom in a Cubic Lattice Absorb Radiation?

[catkin]

[SOLVED] SHM: atom in a lattice

Homework Statement

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

An atom of mass 5 \times 10^{-26} 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

F = ma (Newton 2)
F = -kx (Hooke)
a = -\omega^{2}x (SHM)

The Attempt at a Solution

From Newton 2 and Hooke
a = -kx / m
Substituting in SHM
-kx / m = -\omega^{2}x
\omega = \sqrt{k/m}
= \sqrt{\frac {100} {5 \times 10^{-26}}}
= 4 \times 10^{13} Hz ct1sf

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

 

[Shooting Star]

The ans given is correct. Check your arithmetic.

 

[catkin]

The ans given is correct. Check your arithmetic.

Arithmetic check:
\sqrt{\frac {100} {5 \times 10^{-26}}}
= \sqrt{\frac {100} {5}} \times 10^{13}}
= \sqrt{20}\times 10^{13}}
= 4.472\times 10^{13}}

I still can't see my mistake

 

[catkin]

Ah! f = ω / 2π