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Calculation of the density of a metal by using unit cell dimensions

Silver (atomic weight =108 {u}) has a density of 10.5 {~g} {~c

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Silver (atomic weight $= 108 u$ ) has a density of $10.5 g cm^{- 3} .$ The number of silver atoms on a surface of area $1 0^{- 12} m^{2}$ can be expressed in scientific notation as $y \times 1 0^{x}$ . The value of $x$ is:

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Updated on: Jun 30, 2023

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Benjamin Discussed

Silver (atomic weight

= 108 u

) has a density of

10.5 g cm^{- 3} .

The number of silver atoms on a surface of area

1 0^{- 12} m^{2}

can be expressed in scientific notation as

y \times 1 0^{x}

. The value of

x

is:

8 mins ago

Discuss this question LIVE

8 mins ago

Text solutionVerified

Volume of one mole of silver atoms

= \frac{108}{10.5} cm^{3} / mol

Volume of one silver atom

= \frac{108}{10.5} \times \frac{1}{6.022 \times 1 0 ^{23}} cm^{3}

So,

\frac{4}{3} π r^{3} = \frac{108}{10.5} \times \frac{1}{6.022 \times 1 0 ^{23}} = 1.708 \times 1 0^{- 23}

r^{3} = 0.407 \times 1 0^{- 23} cm^{3} = 0.407 \times 1 0^{- 29} m^{3}

Area of each silver atom,

π r^{2} = π (0.407 \times 1 0^{- 29} m^{3})^{2/3}

So, number of silver atoms in given area

= \frac{1 0 ^{- 12}}{( 0.407 \times 1 0 ^{- 29} m ^{3} ) ^{2/3}} = \frac{1 0 ^{8}}{π \times 2} = 1.6 \times 1 0^{7} = y \times 1 0^{x}

So,

x = 7

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Question Text	Silver (atomic weight $= 108 u$ ) has a density of $10.5 g cm^{- 3} .$ The number of silver atoms on a surface of area $1 0^{- 12} m^{2}$ can be expressed in scientific notation as $y \times 1 0^{x}$ . The value of $x$ is:
Updated On	Jun 30, 2023
Topic	The Solid State
Subject	Chemistry
Class	Class 12
Answer Type	Text solution:1 Video solution: 9
Upvotes	930
Avg. Video Duration	7 min

Silver (atomic weight $= 108 u$ ) has a density of $10.5 g cm^{- 3} .$ The number of silver atoms on a surface of area $1 0^{- 12} m^{2}$ can be expressed in scientific notation as $y \times 1 0^{x}$ . The value of $x$ is:

Text solutionVerified

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Silver (atomic weight $= 108 u$ ) has a density of $10.5 g cm^{- 3} .$ The number of silver atoms on a surface of area $1 0^{- 12} m^{2}$ can be expressed in scientific notation as $y \times 1 0^{x}$ . The value of $x$ is: