Question

Calculate the atomic radius in cm for the following: a. BCC metal with ao = 0.3226 nm. (Enter your answer to three significant figures.) r = cm b. FCC metal with ao = 4.3992 Å. (Enter your answer to three significant figures.) r = cm

Answer 1

Step-by-step explanation:

1) Edge length of the metal in BCC unit cell =
`a=0.33226 nm`

Atomic radius of the metal atom = r

For BCC unit cell, relationship between edge length and radius is given as:

`r=(√(3))/(4)* a=0.4330a`

`r=0.4330* 0.33226 nm=0.144 nm`

`1 nm=10^(-7) cm`

`r=0.144 nm=0.1439* 10^(-7) cm=1.44* 10^(-8) cm[\tex]</p><p><strong>The atomic radius of the metal  atom in BCC unit cell is [tex]1.44 * 10^(-8) cm`.

2) Edge length of the metal in FCC unit cell =
`a=4.3992 \AA`

Atomic radius of the metal atom = r

For FCC unit cell, relationship between edge length and radius is given as:

`r=(1)/(2√(2))* a=0.3535a`

`r=0.3535* 4.3992 \AA=1.56 \AA`

`1 \AA=10^(-8) cm`

`1.56\AA=1.56 * 10^(-8) cm`

The atomic radius of the metal atom in FCC unit cell is
`1.56 * 10^(-8) cm`.