A solid having density of `9 xx 10^(3) kg m^(-3)` forms face centred cubic crystals of edge length `200 sqrt2` pm. What is the molar mass of the solid ? [Avogadro constant `~= 6 xx 10^(23) mol^(-1), pi ~= 3`]

Options

A. `0.0216 kg mol^(-1)`
B. `0.0305 kg mol^(-1)`
C. `0.4320 kg mol^(-1)`
D. `0.4320 kg mol^(-1)`

Answer

B

Explanation

`d = (Z xx M)/(a^3 xx N_A)`
`9 xx 10^(3) = (4 xx M)/((200sqrt(2) xx 10^(-12)m)^(3) xx 6 xx 10^(23))`
`M = (9 xx 10^(3) xx (200sqrt(2))^(3) xx 10^(-36) xx 6 xx 10^(23))/(4)`
`= 0.0305 kg mol^(-1)`.