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The atomic radius (in cm) of an element with a body centred cubit unit cell of molecular weight 137.3 and density 3.62 g cm–3 is:
  • a)
    1.5 × 10–8
  • b)
    1.6 × 10–8
  • c)
    2.2 × 10–8
  • d)
    2.0 × 10–8
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The atomic radius (in cm) of an element with a body centred cubit unit...
First, we need to find the edge length (a) of the body centred cubic unit cell using the density and molecular weight of the element.

Density = mass/volume

Volume of unit cell = a^3

Mass of unit cell = molecular weight/Avogadro's number

Combining these equations:

density = (molecular weight/Avogadro's number) / a^3

a^3 = (molecular weight/Avogadro's number) / density

a^3 = (137.3 g/mol / 6.022 x 10^23 mol^-1) / 3.62 g cm^-3

a^3 = 6.036 x 10^-23 cm^3

a = (6.036 x 10^-23 cm^3)^(1/3)

a = 3.184 x 10^-8 cm

Now, we can find the radius (r) of the atom using the edge length (a) and the geometry of the body centred cubic unit cell.

r = a * sqrt(3) / 4

r = (3.184 x 10^-8 cm) * sqrt(3) / 4

r = 1.386 x 10^-8 cm

Therefore, the atomic radius of the element is approximately 1.386 x 10^-8 cm.
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The atomic radius (in cm) of an element with a body centred cubit unit cell of molecular weight 137.3 and density 3.62 g cm–3 is:a)1.5 × 10–8b)1.6 × 10–8c)2.2 × 10–8d)2.0 × 10–8Correct answer is option 'C'. Can you explain this answer?
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The atomic radius (in cm) of an element with a body centred cubit unit cell of molecular weight 137.3 and density 3.62 g cm–3 is:a)1.5 × 10–8b)1.6 × 10–8c)2.2 × 10–8d)2.0 × 10–8Correct answer is option 'C'. Can you explain this answer? for Chemistry 2024 is part of Chemistry preparation. The Question and answers have been prepared according to the Chemistry exam syllabus. Information about The atomic radius (in cm) of an element with a body centred cubit unit cell of molecular weight 137.3 and density 3.62 g cm–3 is:a)1.5 × 10–8b)1.6 × 10–8c)2.2 × 10–8d)2.0 × 10–8Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Chemistry 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The atomic radius (in cm) of an element with a body centred cubit unit cell of molecular weight 137.3 and density 3.62 g cm–3 is:a)1.5 × 10–8b)1.6 × 10–8c)2.2 × 10–8d)2.0 × 10–8Correct answer is option 'C'. Can you explain this answer?.
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