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The Solid State

Question
CBSEENCH12011120

A metal has a fcc lattice. The edge length of the unit cell is 404 pm. The density of the metal is 2.72 g cm-3. The molar mass of the metal is (NA Avogadro's constant= 6.02 x 1023 mol-1)

  • 40 g mol-1

  • 30 g mol-1

  • 27 g mol-1

  • 20 g mol-1

Solution

C.

27 g mol-1

Given, cell is fcc, So Z =4
Edge length, a = 404 pm = 4.04 x 10-8 cm
Density of metal, d = 2.72 g cm-3
NA = 6.02 x 1023 mol-1
Molar mass ofg the metal, M =?
We know that


density, d=  fraction numerator straight z space straight x space straight M over denominator straight a cubed space straight x space straight N subscript straight A end fraction
therefore space straight M equals space fraction numerator straight d space straight x space straight a cubed space straight x space straight N subscript straight A over denominator straight Z end fraction
space equals fraction numerator 2.72 space xc space left parenthesis 4.04 space straight x space 10 to the power of negative 8 end exponent right parenthesis cubed space straight x space 6.02 space straight x space 10 to the power of 23 over denominator 4 end fraction

space equals 27 space straight g space mol to the power of negative 1 end exponent