Question

The radius of a potassium atom is 231 pm. how many potassium atoms would have to be laid side by side to span a distance of 2.86 mm?

Answer 1

Imagine you place all the potassium atoms side by side. The total length would equal to the sum of all their diameters. Since diameter is twice the radius, the equation for the total distance is:

Total distance = 2rn, where n is the number of potassium atoms
2.86×10⁻³ m = 2(231×10⁻¹² m)(n)
n = 6,190,476.19

So, it would take about 6,190,477 potassium atoms.

Answer 2

Answer:

$6.1905\times 10^{6}$ of potassium atoms are needed.

Explanation:

Radius of the potassium atom,r = 231 pm =$2.31\times 10^{-7} mm$

$1 pm = 10^{-9} mm$

Diameter of the potassium atom = d

$d=2r=2\times 2.31\times 10^{-7} mm=4.62\times 10^{-7} mm$

let the number of potassium atom laid side by side to span a distance of 2.86 mm be x

$x\times d=2.86 mm$

$x\times 4.62\times 10^{-7} mm=2.86 mm$

$x=\frac{2.86 mm}{4.62\times 10^{-7} mm}=6.1905\times 10^{6}$

$6.1905\times 10^{6}$ of potassium atoms would have to be laid side by side to span a distance of 2.86 mm.