Question

The radius of an atom of gold (Au) is about 1.35 Å.

How many gold atoms would have to be lined up to span 9.5 mm ?

Answer 1

Two radius of an atom is equal to the diameter. Adding up all the diameter of the atoms, it should be equal to 9.5 mm. Therefore, we simply convert the units to the same units then divide 1.35 A to 9.5 mm. We calculate as follows:

no. of atoms = 0.0095 m / 1.35x10^-9 m = 7037037 atoms

Hope this answers the question. Have a nice day.

Answer 2

Answer : The number of gold atoms will be,
`3.52* 10^7`

Explanation :

First we have to determine the diameter of an atom of gold.

`Diameter=2* Radius`

Given :

Radius of an atom of gold =
`1.35\AA`

`Diameter=2* 1.35\AA=2.7\AA`

Conversion used :
`(1\AA=10^(-7)mm)`

`Diameter=2.7\AA=2.7* 10^(-7)mm`

Now we have to calculate the number of gold atoms.

`\text{Number of gold atoms}=\frac{\text{Span length}}{\text{Diameter of an atom of gold}}`

`\text{Number of gold atoms}=(9.5mm)/(2.7* 10^(-7)mm)=3.52* 10^7`

Therefore, the number of gold atoms will be
`3.52* 10^7`