Question

1. A structural I beam is made of iron. A view of its cross-section and its dimensions is shown in the figure, where d = 2 cm, w = 29 cm, h = 30 cm and the length (not shown) of the beam is l = 1.29 m. The density of iron is 7560 kg/m3 . The atomic weight of iron is 55.85 g/mol and Avo- gadro number is NA = 6.02214x10^23 /mol.

2. How many atoms are there in this section? Answer in units of atoms.

  

Answer 1

Answer 2

dividing the cross section into 3 parts as shown

the area of cross section = areas of part1 + part2 +part 3

= (w*d)+((h-2d)(d))+(w*d)

= 2(29*2)+( 26*2)

= 168cm²

the area of cross section = 168cm²

the volue of I beam = area * length

= 168*129

= 21672 cm³

= 2.167*10^-2 m³

the volue of I beam = 2.167*10^-2 m³

we know

density = mass/volume

mass = density*volume

= 7560 * 2.167*10^-2  

= 163.84kg

mass of beam = 163.84kg

no of moles of iron = mass of beam /atomic weight

   = 163.84*10³/55.85

   = 2.934 *10³moles

no of moles of iron =2.934*10³ moles

no of atoms = no of moles * N_A

   = 2.934*10³*6.023*10²³

   = 1.767*10²⁷ atoms

1.767*10²⁷ atoms are there in the section

Answer 3