Question

The structure of a sodium chloride (table salt) crystal is shown in the figure below. Each sodium ion Na⁺ has a charge +e and is adjacent to a chloride ion Cl⁻, which has a charge −e. The electric force of attraction between sodium ions and chlorine ions holds the crystal together.

Suppose you attempt to break a cubic salt crystal, 1.26 mm on a side, by applying forces F and −F perpendicular to opposite sides of the cube, trying to pull it apart. How great would F have to be to overcome the attractive forces of all the ions in a 1.5876 mm² plane of the crystal? (Be sure to type in units! Hint: How many ions are in one side? A plane? How much force does each ion apply to each other?)

Answer 1

There are   1.26 * 10^(-3) m / (2.82 10^-10 m/ion) = 4.468 * 10^6 ion pairs in a row trying to "keep things together" and as many rows, so (4.468 * 10^6)^2 = 1.996 * 10^13 ion pairs

As each pair is able to exert a force of 2.89 * 10-9 N, we have to apply a force of

1.996 * 10^13 ion pairs* 2.89 * 10-9 N = 57,695 N.

Since we are pulling on both sides with F, F = 57695/2

= 28.84 kN