Question

The sensitivity of your balance (laboratory scale) is 1 microgram. What is the thinnest 1 mm x 1 mm that could be weighed accurately? What is the smallest number of iron atoms (in a pure iron sample) that the scale above could accurately weigh?

Answer 1

The smallest amount that the balance can measure ,

m = 1 microgram = 1 ×10^-9 kg.

Volume (V)=

The smallest volume that can measure using the balance, V

(1 * 10^-3 m)× (1 * 10^-3 m)× (x * 10^-3 m) =  

therefore the thickness of smallest 1mm×1mm , ie. x , can be solved out from above equation.

x = d^-1 × 10^-2 mm

Let us calculate the minimum number of atoms that the balance can accurately weigh(N).

For BCC lattice structure,

lattice parameter a

radius of iron atom r

so the relationship between a and r for bcc lattice  

Number of atoms in a bcc unit cell = 2

therefore total numbers of iron atoms that can measure , N