Step by step solution to "If the atomic radius of lead is 0.175..."

High School
Geometry
High school geometry
Circles

Braxton Pugh

Answered question

2021-09-14

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

Answer & Explanation

Roosevelt Houghton

Skilled2021-09-15Added 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} (1)

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}

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