Question

Calculate the number of atoms in a 1 inch diameter 4 foot long tube of boron

Answer 1

given -- height of tube = 4 foot , diameter of tube = 1 inch , 1inch = 0.0254m , 1 foot = 0.305 m and π = 3.14(assume)

Total volume of boron tube =( π/4)×d×d×h

where d is diameter of tube = 1 inch = 1×0.0254m = 0.0254m

and h is height of tube = 4 foot = (4×0.305)m= 1.22m

So , volume of tube = (3.14×0.0254×0.0254×1.22)/4 = 0.000617 m^3

Now , volume of 1 boron atom = (4/3)× π × r×r×r

where r is the atomic radii of 1 boron atom which is equal to 85 pm= 85×10^(-12)m

so , volume of 1 boron atom = (4*3.14*[85*10^(-12)]^3)/3

= 2.5711× 10^(-30) m3

so , number of atoms of boron in the tube will be=( volume of tube/volume of 1 boron atom in that tube)

= 0.000617 m3 / 2.5711× 10^(-30) m3

= 2.4 × 10^(26) atoms of boron