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

What is the number of unit cells when one mole atom of a metal that forms simple cubic structure?

A. $6.022 \times 10^{23}$

B. $1.204 \times 10^{24}$

C. $9.033 \times 10^{23}$

D. $3.011 \times 10^{23}$

Correct Option is (A)

Number of atoms in one mole of atom of a metal $= 6.022 \times 10^{23}$

Number of atoms in a simple cubic unit cell $= 1$

$∴$ Number of unit cells $= 6.022 \times 10^{23}$

7. ⇒ (MHT CET 2021 21th September Evening Shift )

What is the total number of atoms in BCC crystal lattice having $1.8 \times 10^{20}$ unit cells?

A. $9.0 \times 10^{20}$

B. $1.8 \times 10^{20}$

C. $3.6 \times 10^{20}$

D. $7.2 \times 10^{20}$

Correct Option is (C)

For $BCC$ unit cell, $n = 2$

$∴$ Total number of atoms in $1.8 \times 10^{20}$ unit cells $= 2 \times 1.8 \times 10^{20} = 3.6 \times 10^{20}$ atoms

8. ⇒ (MHT CET 2021 21th September Evening Shift )

What is the percentage of unoccupied volume in BCC structure?

A. 32%

B. 74%

C. 26%

D. 68%

Correct Option is (A)

68% of the total volume in bcc unit lattice is occupied by atoms and 32% is empty space or unoccupied volume.

9. ⇒ (MHT CET 2021 21th September Morning Shift )

What is the percentage efficiency of packing in BCC structure?

A. 32%

B. 74%

C. 26%

D. 68%

Correct Option is (D)

The percentage efficiency of packing in BCC structure is 68%.

10. ⇒ (MHT CET 2021 21th September Morning Shift )

An element with simple cubic close structure has edge length of unit cell $3.86 \overset{o}{A}$ . What is the radius of atom?

A. $5.79 \times 10^{- 8} cm$

B. $1.93 \times 10^{- 8} cm$

C. $3.86 \times 10^{- 8} cm$

D. $2.43 \times 10^{- 8} cm$

Correct Option is (B)

a = $3.86 \overset{o}{A} = 3.86 \times 10^{- 8}$ cm, r = ?

For simple cubic close structure,

$r = \frac{a}{2} = \frac{3.86 \times 10^{- 8}}{2} = 1.93 \times 10^{- 8}$ cm

⇒Solid State