SOLID STATE PHYSICS EXAM 2025/2026
QUESTIONS AND ANSWERS 100% PASS
Define Avogadro's number. - ANS 10²³, number of atoms in 1 cm³ of a crystalline solid.
Define a lattice. - ANS Set of points generated by multiples of generating vectors.
Define a primitive unit cell. - ANS The volume of space which, when translated through all of
the vectors of the Bravais lattice, fills space without overlapping or leaving any voids. It contains
only one lattice point.
Define a Wigner-Seitz cell. - ANS A primitive unit cell. The region of space which is closer to
one given lattice point than any other.
Define a non-primitive unit cell. - ANS Contains more than one lattice point. Fills space
without overlap by using some subset of the primitive vectors.
Define a basis. - ANS What is placed on each lattice site.
Name 2 close-packed structures. - ANS Face-centred cubic
Hexagonal close-packed
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, Give the simple cubic primitive vectors. - ANS a₁=ax
a₂=ay
a₃=az
Give the body-centred cubic primitive vectors. - ANS a₁=a/2(x+y-z)
a₂=a/2(-x+y+z)
a₃=a/2(x-y+z)
Give the face-centred cubic primitive vectors. - ANS a₁=a/2(x+y)
a₂=a/2(y+z)
a₃=a/2(z+x)
Give the hexagonal close-packed primitive vectors. - ANS a₁=a(x/2-√3/2y)
a₂=a(x/2+√3/2y)
a₃=cz
Give 2 assumptions made when using X-ray diffraction to determine crystal structures. -
ANS X-rays only scatter once (kinematic approximation) because they interact weakly with
the charge distribution in a solid.
The source of X-rays and the detector are sufficiently far away from the sample so we can
assume the ingoing and outgoing waves as plane waves.
Explain the Bragg theory of diffraction and give an assumption made. - ANS Two waves
specularly reflected by successive planes. For constructive interference, require Bragg condition
nλ=2dsin(θ). We assume the planes to be uniform in comparison to the wavelength of X-rays.
Define lattice planes. - ANS Planes that contain at least 3 non-colinear points of a given
Bravais lattice.
2 @COPYRIGHT 2025/2026 ALLRIGHTS RESERVED
QUESTIONS AND ANSWERS 100% PASS
Define Avogadro's number. - ANS 10²³, number of atoms in 1 cm³ of a crystalline solid.
Define a lattice. - ANS Set of points generated by multiples of generating vectors.
Define a primitive unit cell. - ANS The volume of space which, when translated through all of
the vectors of the Bravais lattice, fills space without overlapping or leaving any voids. It contains
only one lattice point.
Define a Wigner-Seitz cell. - ANS A primitive unit cell. The region of space which is closer to
one given lattice point than any other.
Define a non-primitive unit cell. - ANS Contains more than one lattice point. Fills space
without overlap by using some subset of the primitive vectors.
Define a basis. - ANS What is placed on each lattice site.
Name 2 close-packed structures. - ANS Face-centred cubic
Hexagonal close-packed
1 @COPYRIGHT 2025/2026 ALLRIGHTS RESERVED
, Give the simple cubic primitive vectors. - ANS a₁=ax
a₂=ay
a₃=az
Give the body-centred cubic primitive vectors. - ANS a₁=a/2(x+y-z)
a₂=a/2(-x+y+z)
a₃=a/2(x-y+z)
Give the face-centred cubic primitive vectors. - ANS a₁=a/2(x+y)
a₂=a/2(y+z)
a₃=a/2(z+x)
Give the hexagonal close-packed primitive vectors. - ANS a₁=a(x/2-√3/2y)
a₂=a(x/2+√3/2y)
a₃=cz
Give 2 assumptions made when using X-ray diffraction to determine crystal structures. -
ANS X-rays only scatter once (kinematic approximation) because they interact weakly with
the charge distribution in a solid.
The source of X-rays and the detector are sufficiently far away from the sample so we can
assume the ingoing and outgoing waves as plane waves.
Explain the Bragg theory of diffraction and give an assumption made. - ANS Two waves
specularly reflected by successive planes. For constructive interference, require Bragg condition
nλ=2dsin(θ). We assume the planes to be uniform in comparison to the wavelength of X-rays.
Define lattice planes. - ANS Planes that contain at least 3 non-colinear points of a given
Bravais lattice.
2 @COPYRIGHT 2025/2026 ALLRIGHTS RESERVED
