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