1. ⇒ (MHT CET 2023 11th May Morning Shift )

Which formula is used to calculate edge length in bcc structure?

A. $a = \frac{\sqrt{3} r}{4}$

B. $a = \frac{4}{\sqrt{3} r}$

C. $a = \frac{\sqrt{3}}{4 r}$

D. $a = \frac{4 r}{\sqrt{3}}$

Correct Option is (D)

Currently no explanation available

2. ⇒ (MHT CET 2023 10th May Evening Shift )

Find the radius of an atom in fcc unit cell having edge length $393 pm$ .

A. $196.51 pm$

B. $170.22 pm$

C. $78.63 pm$

D. $138.93 pm$

Correct Option is (D)

For fcc crystal structure,

$\begin{aligned} 4 r & = \sqrt{2} a \\ ∴ r & = \frac{\sqrt{2} a}{4} = \frac{1.414 \times 393}{4} = 138.93 pm \end{aligned}$

3. ⇒ (MHT CET 2023 10th May Morning Shift )

Calculate the edge length of unit cell of metal which crystallises to bec structure.

(Radius of metal atom $= 173 pm$ )

A. $5.01 \times 10^{- 8} cm$

B. $4.00 \times 10^{- 8} cm$

C. $4.5 \times 10^{- 8} cm$

D. $5.5 \times 10^{- 8} cm$

Correct Option is (B)

For bcc unit cell, $r = \frac{\sqrt{3}}{4} a$

$\begin{aligned} ∴ a = \frac{4 r}{\sqrt{3}} = \frac{4 \times 173}{1.73} & = 400 pm \\ = 400 \times 10^{- 10} cm \\ = 4.00 \times 10^{- 8} cm \end{aligned}$

4. ⇒ (MHT CET 2023 9th May Evening Shift )

Find the radius of metal atom in simple cubic unit cell having edge length 334.7 pm?

A. $167.35 pm$

B. $334.70 pm$

C. $144.93 pm$

D. $118.32 pm$

Correct Option is (A)

For simple cubic unit cell $r = \frac{a}{2} = \frac{334.7 pm}{2} = 167.35 pm$

For simple cubic unit cell, radius is half of the edge length.

5. ⇒ (MHT CET 2023 9th May Morning Shift )

What is the packing efficiency of silver metal in its unit cell?

A. $52.4 %$

B. $68.0 %$

C. $32.0 %$

D. $74.0 %$

Correct Option is (D)

Silver has fcc crystal structure. Packing efficiency of fcc unit cell is 74.0%.

⇒Solid State