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Tungsten crystallizes in a body-centered cubic unit cell with an edge length of 3.165 A.(a) What is the atomic radius of tungsten in this structure?(b) Calculate the density of tungsten.
a) 1.37 $\mathrm{A}$b) 19.65 $\mathrm{gcm}^{-3}$
02:31
Aadit S.
Chemistry 102
Chapter 10
Liquids and Solids
Liquids
Solids
University of Central Florida
Rice University
Drexel University
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Lectures
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in this podcast, we're gonna be discussing the lattice structures of various different crystalline solids. So the first thing we're taking a look at is the radius. So our equation here is our is equal to route three a over four after we've rearranged it, and so we can plug in some values. So we have our is equal to roots. Three multiplied by 3.165 Armstrong invited by four. So this is equal to 1.37 Armstrong. So that is the atomic radius of tungsten and a body centered cubic unit cell. Next, we can take a look at the density of tank stone. So in a body centered cubic units are 18 tungsten atoms present when each of the eight corners so start fresh paid to have eight multiplied by 1/8, gives us one atom on one tungsten atoms present at the center. So we add one atom. Give us two atoms next week in take a look at the Mullah mass of tungsten. That's 183.84 g and the number of atoms in one mole of tungsten, a 6.22 times 10 to 23. Do that for Juan Tungsten Unit Cell, equal to 61.5 six times 10 tonight it's a 23 g. So if we take a look at the volume next where it B is equal to a cube. So we have 3.165 times, 10 to the minus eight centimeters cube. That gives us a value off 31 went 705 times 10 to the negative. 24 Santa made this cute. Next, the density of tungsten could be calculated where we can have density. Tungsten. It's equal to 61.56 times, 10 to the negative 23 g. Divide that by 31.705 times 10 to the negative 24 centimeters cube. That gives us a value of 19.65 g per centimeters Cute.
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