Physical Chemistry> solids...

What is the packing efficiency of a two dimensional square unit cell?

Ans-78.54%

how??

lipika sahoo , 13 Years ago

Grade 12

3 Answers

Saurabh Anand

in 2 dimensional.....a unit cell square contains 4 circles each having 1/4 contribution to the unit cell(we are talking about circle bcoz it is the case of 2-D not 3-D)....so effective no of circle will be 1 and area of circle is πr²....and 2r=a where a is the side of unit square cell....now use packing efficiency formula and u will get the answer..

Approved

Last Activity: 13 Years ago

kamlesh

Area of square=L²

4R=√2L

R=L/2√2

% packing fraction=area of circle*100/area of square

2*πR²/L²

= 78.5%

Last Activity: 7 Years ago

Rishi Sharma

Dear Student,
Please find below the solution to your problem.

The diagonal is given as 4r, where r is the radius of an atom.
Diagonal = √L^2 + L^2 = √2L
4r = √2Lor L = 4r/√2
Total area = L^2
or(4r/√2)^2 = 8r2
Number of spheres inside the square is
1 + 4(0.25) = 2
Area of each sphere = πr^2
Total area of spheres = 2×πr^2
Packing fraction = Totalareaofspheres/Totalarea
= 2×πr2/8r^2
= π/4
= 0.785
So, the percentage fraction is 78.5%

Thanks and Regards

Last Activity: 5 Years ago