How many Rb atoms to fit on a 9Cm^2 square?

[UnD3R0aTh]

1. The problem is in the attachments



2. Basic chemistry knowledge



3. The radius of one Rb atom is 4.95/2 time 10^-8 cm, we calculate the area then divide 9 into the area of one atom, we get the number of atoms, why is 4.7 x 10^15 atoms wrong?

 

[mfb]

There are empty spaces between the atoms - they need more space than just pi*r².

 

[UnD3R0aTh]

exactly my thought, how to calculate that?!

 

[mfb]

Does this sketch help?

 

[UnD3R0aTh]

excellent, i solved the first one, but the second one I'm not really sure how to calculate the side of the triangle that's enclosing one atom!

 

[mfb]

You can draw an equilateral triangle in the lattice.

 

[UnD3R0aTh]

yes but it looks like it's side is longer than the diameter, how to calculate it's length?!

 

[UnD3R0aTh]

no wait, the triangles do not work, they overlap! parallelograms work! how to calculate the area of a parallelogram using it's sides?

 

[mfb]

Then you are drawing the wrong triangles. Use the centers of the atoms, this is easier. Afterwards, find out how many atoms per triangle (or triangles per atom) you have.

 

[UnD3R0aTh]

can u please draw a diagram like u did with the first one?

 

[mfb]

Can you show your diagram?

 

[UnD3R0aTh]

i don't know to how to draw this, using what program?

 

[mfb]

Every drawing program can draw lines. Windows always comes with Paint, for example.

 

[UnD3R0aTh]

pffffft I've been thinking about this problem for far too long I'm at my wits end, i really need to stop wasting my time with this and study, i feel nervous already cause i wasted so much time, please give me a more strong hint, save me some time, thank you

 

[UnD3R0aTh]

solved it