MTL 200 FINAL EXAM STUDY GUIDE – 2025/2026 (Questions & Verified Answers)

1


MTL 200 FINAL EXAM STUDY GUIDE – 2025/2026 (Questions &

Verified Answers)




1. How many atoms are present in a BCC unit cell?

a) 1

b) 2

c) 4

d) 8

Explanation: BCC (Body-Centered Cubic) has 1 atom at each corner

(1/8 contribution × 8) plus 1 atom at the center = 2 atoms.




2. How many atoms are present in an FCC unit cell?

a) 2

b) 4

c) 6

d) 8

, 2


Explanation: FCC (Face-Centered Cubic) has 1/8 atom at each corner ×

8 + 1/2 atom at each face × 6 = 4 atoms.




3. What is the relationship between the atomic radius (R) and edge

length (a) in BCC?

a) 2R = a

b) 4R = √3 a

c) 4R = √2 a

d) 2R = √2 a

Explanation: In BCC, the body diagonal = 4R = √3 × a.




4. What is the relationship between the atomic radius (R) and edge

length (a) in FCC?

a) 2R = a

b) 4R = √3 a

, 3


c) 4R = √2 a

d) 2R = √3 a

Explanation: In FCC, the face diagonal = 4R = √2 × a.




5. Which formula calculates the Atomic Packing Factor (APF)?

a) Volume of unit cell / volume of atoms

b) Volume of atoms / volume of unit cell

c) Volume of atoms × volume of unit cell

d) Number of atoms / volume of unit cell

Explanation: APF = (Volume occupied by atoms in a unit cell) / (Total

volume of unit cell).




6. What is the formula to calculate material density in a crystal?

a) (n × A) / (Vc × Na)

b) (Vc × Na) / (n × A)

, 4


c) (n × Vc) / (A × Na)

d) (A × Na) / (n × Vc)

Explanation: Density = (Number of atoms per unit cell × Atomic mass) /

(Unit cell volume × Avogadro’s number).




7. In terms of diffraction, Bragg’s Law is expressed as:

a) nλ = d sin θ

b) nλ = 2 d sin θ

c) nλ = 2d cos θ

d) λ = 2 d sin θ

Explanation: Bragg’s Law relates wavelength λ, interplanar spacing d,

and diffraction angle θ: nλ = 2d sin θ.




8. What must you do to the diffraction angle θ given in experiments to

use in Bragg’s formula?

a) Multiply by 2