Question

What’s the number of gold atoms in a nanogram? a picogram?

Answer 1

The number of gold atoms in nanogram is,
`3.057* 10^(12)`

The number of gold atoms in picogram is,
`3.057* 10^(9)`

Explanation :

As we know that the molar mass of gold is, 196.97 g/mole. That means, 1 mole of gold has 196.97 grams of mass of gold.

As we know that,

1 mole contains
`6.022* 10^(23)` number of atoms.

First we have to determine the number of gold atoms in a nanogram.

As, 196.97 grams of gold contains
`6.022* 10^(23)` number of gold atoms

And, 1 grams of gold contains
`(1g)/(196.97g)* (6.022* 10^(23))` number of gold atoms

So,
`10^(-9)` nanograms of gold contains
`(1g)/(196.97g)* (10^(-9))* (6.022* 10^(23))=3.057* 10^(12)` number of gold atoms

The number of gold atoms in nanogram is,
`3.057* 10^(12)`

Now we have to determine the number of gold atoms in a picogram.

As, 196.97 grams of gold contains
`6.022* 10^(23)` number of gold atoms

And, 1 grams of gold contains
`(1g)/(196.97g)* (6.022* 10^(23))` number of gold atoms

So,
`10^(-12)` picograms of gold contains
`(1g)/(196.97g)* (10^(-12))* (6.022* 10^(23))=3.057* 10^(9)` number of gold atoms

The number of gold atoms in picogram is,
`3.057* 10^(9)`