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Q.

A solid element- -(monoatomic) exist.s as cubic crystal. If its atomic radius is $1.0 Å$ and the ratio of packing fraction and density is 0.1 ${cm}^{3}$ /gm. then the atomic mass oft.be element is: $(N_{A} = 6 \times 10^{23})$

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a

$16 π$

b

$8 π$

c

$4 π$

d

$80 π$

answer is A.

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Detailed Solution

$\frac{P.F.}{d} = \frac{V_{particle} / V_{unit cell}}{m_{particle} / V_{unit cell}} = \frac{V_{particle}}{m_{particle}}$

or, $0.1 = \frac{Z \times \frac{4}{3} π {(1.0 \times 10^{- 8})}^{3}}{Z \times M / 6 \times 10^{23}}$

$\Rightarrow M = 8 π$

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A solid element- -(monoatomic) exist.s as cubic crystal. If its atomic radius is 1.0 Å and the ratio of packing fraction and density is 0.1 cm3/gm. then the atomic mass oft.be element is: NA=6×1023