Chemistry, asked by StrongGirl, 7 months ago

In a solid substance edge length of unit cell is 405 pm. density of solid is 10.9 gram/cm^3 and molar mass of substance is 109 gram then find radius of atom which form this unit cell in pm ?

Answers

Answered by Anonymous
3

Answer:

Given:-

  • Length of unit cell (l) = 405 pm or 405×10^-10cm

  • Density (ρ) = 10.9 g/cm³

  • Molar mass (M) = 109 g

Formula:

Density of unit cell,

 \bf \large \rho =  \frac{Z × M }{N_o× {a}^{3} }

Substitute the value in Equation,

 \bf \large \longmapsto \: 10.9 = \frac{Z \times 109}{6.02 \times  {10}^{23}  \times (405 \times  {10}^{10}) ^{3}  }   \\  \\

 \bf \large \longmapsto \: 10.9 = \frac{Z \times 109}{6.02 \times  {10}^{23}  \times 66430125 \times  {10}^{ - 30}  }   \\  \\  \bf \large \longmapsto \: 10.9 =  \frac{Z \times 2.72 \times  {10}^{ - 7} }{ {10}^{ - 7} }  \\  \\  \bf \large \longmapsto \: Z =  \frac{10.9}{2.72}  \\  \\ \bf \large \longmapsto \: Z =4

We know that,

 \sf \large { r =  \frac{ \sqrt{2}a }{4} }

Substitute value of a in the equation,

 \bf  \large : \longmapsto \: r =  \frac{ \sqrt{2}  \times 405}{4}  \\  \\  \bf  \large : \longmapsto \: r =143.2 \:  \: pm

  \bf \large \underline  \blue{Radius  \:  \: of  \:  \: atom \:  \:  (r) \:  \:  = \:  \:  143.2 \:  \:  pm}

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