Tungsten has a density of 19.35 g `cm^(-3)` and the length of the side of the unit cell is 316 pm. The unit cell is a body centred unit cell. How many atoms does 50 grams of the element contain?

Answer

`1.64xx10^(23)` atoms

Explanation

Step I. Calcualtion of mass of an atom of tungsten.
Let the mass of the atom of tungsten metal = m gram.
Mass of the unit cell `=2xxm=2` m gram.
Edge length (a) = 316 pm = `316xx10^(-10)cm`
Volume of the unit cell `(a^(3))=(316xx10^(-10))^(3)cm^(3)=31.55xx10^(-24)cm^(3)`
`"density of unit cell"=("Mass of unit cell")/("Volume of unit cell")or (19.35"g cm"^(-3))=(("2 m gram"))/((31.55xx10^(-24)cm^(3)))`
`m=1//2xx(19.35"g cm"^(-3))xx(31.55xx10^(-24)cm^(3))=30.529xx10^(-23)g.`
Step II. Calculation of the number of atoms in 50 grams of tungsten.
`"No. of atoms"=("Mass of tungsten")/("Mass of ne atom of tungsten")=((50 g))/((35.529xx10^(-23)g))=1.64xx10^(23)"atoms."`