A metal crystallizeds in cubic close packed ( ccp). The atomic radius of metal is 144 pm and its atomic mass is 197 a.m.u. Its density is

Options

A. 19.4 `g cm^(-3)`
B. `1.94 g cm^(-3)`
C. `29.4 g cm^(-3)`
D. `2.94 g cm^(-3)`

Answer

A

Explanation

For ccp arrangement
`a = 2 sqrt( 2) r = 2 xx 1.414 xx 144 `
`= 407.2`pm = `407.2 xx 10^(-10)`cm
`d = ( Z xx M )/( a^(3) xx N_(O))`
`= ( 4 xx 197)/((407.2 xx 10^(-10))^(3) xx ( 6.02 2 xx 10^(23)))`
`= 19.4g cm^(-3)`