If the atomic radius of lead is 0.175 nm, calculate the volume of its unit cell in cubic meters

Braxton Pugh
2021-09-14
Answered

If the atomic radius of lead is 0.175 nm, calculate the volume of its unit cell in cubic meters

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Roosevelt Houghton

Answered 2021-09-15
Author has **106** answers

Given

We are given the radius of lead atom R= 0.175 nm. We are asked to calculate the volume of the unit cell crystal structure of the lead$V}_{c$ in cubic meters.

Solution

To calculate the volume of the unit cell we should know the crystal structure unit cell shape, where lead has FCC crystal structure (See Table 3.1) on page 54, where the volume of FCC crystal structure is given by equation 3.6 by

${V}_{c}=16{R}^{3}\sqrt{2}\text{}\text{}\text{}\left(1\right)$

Now we can plug the vlaue for R in equation (1) to get$V}_{c$ where R will be in (m)

$V}_{c}=16{R}^{3}\sqrt{2$

$=16{(0.175\times {10}^{-9}m)}^{3}\sqrt{2}$

$=1.21\times {10}^{-28}{m}^{3}$

Result

$V}_{c}=1.21\times {10}^{-28}{m}^{3$

We are given the radius of lead atom R= 0.175 nm. We are asked to calculate the volume of the unit cell crystal structure of the lead

Solution

To calculate the volume of the unit cell we should know the crystal structure unit cell shape, where lead has FCC crystal structure (See Table 3.1) on page 54, where the volume of FCC crystal structure is given by equation 3.6 by

Now we can plug the vlaue for R in equation (1) to get

Result

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