Question

A solid element (monoatomic) exists in cubic crystal. If its atomic radius is 1.0 Å and

the ratio of packing fraction and density is 0.1 cm3
/g, then the atomic mass of the

element is (NA = 6 x 1023)

​

Answer 1

Answer:

25.12 g is the answer

Explanation:

refer attachment for explanation!!

Answer 2

Thus, the atomic mass of the element is 25.12 grams.

Given:

A solid element (monoatomic) exists in a cubic crystal. If its atomic radius is 1.0 Å and the ratio of packing fraction and density is 0.1 cm3/g.

To find:

The atomic mass of the element.

Solution:

Packing a fraction of an element is given as-

$= \frac{4\pi {r}^{3}z }{3 {a}^{3} }$

Where z is the number of atoms per unit cell and $a^3$ is the volume of the solid.

Again density of the element is given as-

$d = \frac{zm}{N×a^3}$

The ratio of packing fraction and density is 0.1 cubic cm and r is $10^{-8}$ cm.

$\frac{p.f}{d} = \frac{4\pi {r}^{3} z}{3 {a}^{3} } \times \frac{N×a^3}{zm} \\0.1=\dfrac{4×3.14×(10^{-8})^3×6×10^{23}}{3m}\\m=25.12$

Thus, the atomic mass of the element is 25.12 grams.

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