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JEE Advanced levelOne or more correct optionsDifficulty 3 of 3ss045

Three metals X (simple cubic), Y (bcc) and Z (fcc) have the same atomic radius and the same atomic mass. Which statements about their densities are correct?

A $ρ_{Z} / ρ_{X} \approx 1.41$
B $ρ_{Y} / ρ_{X} \approx 1.30$
C $ρ_{Z} / ρ_{Y} \approx 1.50$
D $ρ_{Y} > ρ_{Z}$

Answer: A, B

For equal

r

and

M

,

ρ \propto Z / a^{3}

: simple cubic

1/ (2 r)^{3} = 0.125/ r^{3}

; bcc

2/ (4 r / 3)^{3} = 0.1624/ r^{3}

; fcc

4/ (22 r)^{3} = 0.1768/ r^{3}

. Ratios:

Z / X = 1.414

,

Y / X = 1.299

,

Z / Y = 1.089

. So the first two hold, and

ρ_{Z} > ρ_{Y}

.

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