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Question

The density of metal which crystallises in bcc lattice with unit cell edge length 300 pm and molar mass 50 g mol-1 will be


A

6.15 g cm-3

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B

9.31 g cm-3

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C

10.0 g cm-3

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D

14.2 g cm-3

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Solution

The correct option is A

6.15 g cm-3


The explanation for the correct answer:-

Option (A) 6.15gcm-3

Step 1: Given data

In a body-centred cubic unit cell, the number of atoms in a unit cell, z is equal to two.

Unit Cell is the smallest part (portion) of a crystal lattice. It is the simplest repeating unit in a crystal structure.

The entire lattice is generated by the repetition of the unit cell in different directions.

n=2 and Unit cell edge lengtha=300×10-10cm

M=50g

Step 2: Formula used

ρ=nMNoa3g/cm3

Step 3: Deriving theoretical density

The density of unit cell = 2×Ma3×NA

ρ=2×506.022×1023×3003×(10-10)3ρ=6.15g/cm3

Hence, option (A) is the correct answer.


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