Question

The packing fraction in two dimensional square packing structure is (R: radius of atom)
1) πR^2\(2R) × (2R)
2) π\(2R) × (2R)
3) R^2\(2R) × (2R)
4) π+3R^2)\ R×(2R)​

Answer 1

Answer: option 1st…

Explanation:

Answer 2

The packing fraction in two-dimensional square packing structure is πR^2\(2R) × (2R).

Calculations

The diagonal for Square packing structure is 4R, (r is the radius).

Diagonal = $\sqrt{L^{2} + L^{2} )} =\sqrt{2L}$

Using the above 2 statements,

  4R =$\sqrt{2L}$

= $\sqrt{2L}$ = 4R

 = L = 4R/$\sqrt{2}$

Total Area = $L^{2}$

                 = $(4R/\sqrt{2} )^{2}$

                 = 8R²

Number of spheres inside square = 1 + 4(1/4)

                                                        =   1 + 1

                                                        =    2

Area of sphere = πR²

Area of 2 spheres = 2 x πR²

Packing fraction = Area of 2 spheres/ Total area

                           =  (2 x πR²) / 8R²

                           =  πR² / 4R²

                           = πR² / (2R x 2R)