Question

Gold has a face-centered cubic arrangement with a unit cell edge length of 4.08 Å . How many moles of gold fit in a gold nanoparticle sheet with a length of 82.8 nm , a width of 28.6 nm , and a thickness of 9.44 nm ?

Answer 1

Answer

2.19 ×10^-18 mol

Explanation

Unit cell edge length = 4.08A^{​​​​​​}= 0.408nm

volume of Unit cell = (0.408nm)³ =0.067917nm³

Volume of nonoparticle sheet = 82.8nm × 28.6nm × 9.44nm = 22355nm³

Number of unit cells in nanoparticle sheets = 22355nm³/0.067917nm³ = 329152 unit cells

Number of atoms in a face centred unit cell = 4

Numer of gold atoms in the nano sheet = 329152 × 4 = 1316608atoms

1mole = 6.022×10²³ atoms

Number of moles of Gold fit to the nano sheet = (1mol/6.022×10²³atoms) × 1316608atoms = 2.19× 10^-18mol