Question

In: Physics

The atomic mass number of copper is 64. Assume that atoms in solid copper form a...

The atomic mass number of copper is 64. Assume that atoms in solid copper form a cubic crystal lattice. To visualize this, imagine stacking tiny sugar cubes into a big cube. If you pretend there is a copper atom in the middle of each sugar cube, then dissolve the sugar away, the copper forms a cubic lattice. What is the smallest distance between copper atoms?

Hint: The answer is 0.228nm, but you must still show all your work with clear understanding!

Solutions

Expert Solution

Density of copper

Atomic mass number of copper is . That is mass of one mole of copper atoms is .

One mole of copper atoms means one Avogadro number of copper atoms.

Hence atoms weigh .

Volume of one mole of copper atoms is

Smallest distance between copper atoms is equal to size of one unit cell (tiny sugar cube)

Let this size be . Hence each atom occupies a volume .

Volume occupied by one mole of copper atoms is

Hence

Hence smallest distance between copper atoms is

genius_generous answered 2 years ago
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