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Solid State formulas

Master Solid State through 22 JEE Advanced-level formulas, systematically structured with every variable spelled out. Revise concept-wise, identify the areas where you need improvement, and focus your preparation with greater precision.

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Solid State, every formula

22 formulas, typeset and free. Print it, or keep it open beside your practice.

Density of a unit cell
$ρ = \frac{Z M}{a ^{3} N _{A}}$
Q1MCQDensity
The density of a cubic unit cell is:
- A
  $\dfrac{ZM}{a^{3}N_A}$
- B
  $\dfrac{a^{3}N_A}{ZM}$
- C
  $ZMa^{3}$
- D
  $\dfrac{M}{a^{3}}$
Atoms in simple cubic
$Z = 1$
Atoms in BCC
$Z = 2$
Atoms in FCC
$Z = 4$
Edge–radius (simple cubic)
$a = 2 r$
Q1MCQEdge SC
For a simple cubic cell, the edge length is:
- A
  $2r$
- B
  $\dfrac{4r}{\sqrt3}$
- C
  $2\sqrt2 r$
- D
  $r$
Edge–radius (BCC)
$a = \frac{4 r}{3}$
Q1MCQEdge BCC
For a BCC cell, the edge length is:
- A
  $\dfrac{4r}{\sqrt3}$
- B
  $2r$
- C
  $2\sqrt2 r$
- D
  $4r$
Edge–radius (FCC)
$a = 22 r$
Q1MCQEdge FCC
For an FCC cell, the edge length is:
- A
  $2\sqrt2 r$
- B
  $2r$
- C
  $\dfrac{4r}{\sqrt3}$
- D
  $4r$
Packing efficiency (SC)
$52.4%$
Q1MCQPacking SC
The packing efficiency of a simple cubic lattice is:
- A
  $52.4\%$
- B
  $68\%$
- C
  $74\%$
- D
  $100\%$
Packing efficiency (BCC)
$68%$
Q1MCQPacking BCC
The packing efficiency of a BCC lattice is:
- A
  $68\%$
- B
  $52.4\%$
- C
  $74\%$
- D
  $50\%$
Packing efficiency (FCC/HCP)
$74%$
Q1MCQPacking FCC
The packing efficiency of an FCC/HCP lattice is:
- A
  $74\%$
- B
  $68\%$
- C
  $52.4\%$
- D
  $100\%$
Coordination number (SC)
$6$
Coordination number (BCC)
$8$
Coordination number (FCC)
$12$
Octahedral voids
$number = N (= number of atoms)$
Q1MCQOctahedral voids
The number of octahedral voids in a close-packed structure of $N$ atoms is:
- A
  $N$
- B
  $2N$
- C
  $\dfrac{N}{2}$
- D
  $4N$
Tetrahedral voids
$number = 2 N$
Q1MCQTetrahedral voids
The number of tetrahedral voids for $N$ atoms is:
- A
  $2N$
- B
  $N$
- C
  $\dfrac{N}{2}$
- D
  $4N$
Radius ratio (octahedral)
$0.414 - 0.732$
Q1MCQRadius ratio (oct)
For an octahedral void, the radius ratio range is:
- A
  $0.414$–$0.732$
- B
  $0.225$–$0.414$
- C
  $0.732$–$1$
- D
  $0$–$0.155$
Radius ratio (tetrahedral)
$0.225 - 0.414$
Q1MCQRadius ratio (tet)
For a tetrahedral void, the radius ratio range is:
- A
  $0.225$–$0.414$
- B
  $0.414$–$0.732$
- C
  $0.732$–$1$
- D
  $0$–$0.155$
Bragg's law
$nλ = 2 d sin θ$
Q1MCQBragg
Bragg's law of X-ray diffraction is:
- A
  $n\lambda=2d\sin\theta$
- B
  $n\lambda=d\sin\theta$
- C
  $n\lambda=2d\cos\theta$
- D
  $\lambda=d$
Number of atoms per unit volume
$n = \frac{Z}{a ^{3}}$
Q1MCQAtoms per volume
The number of atoms per unit volume is:
- A
  $\dfrac{Z}{a^{3}}$
- B
  $\dfrac{a^{3}}{Z}$
- C
  $Za^{3}$
- D
  $\dfrac{Z}{a}$
Frenkel defect
$ion displaced to interstitial site (density unchanged)$
Q1MCQFrenkel
In a Frenkel defect, the density of the crystal:
- A
  remains unchanged
- B
  decreases
- C
  increases
- D
  becomes zero
Schottky defect
$cation + anion vacancy (density decreases)$
Q1MCQSchottky
In a Schottky defect, the density of the crystal:
- A
  decreases
- B
  increases
- C
  stays the same
- D
  doubles
Body diagonal (BCC)
$3 a = 4 r$
Q1MCQBody diagonal BCC
For a BCC cell, the body diagonal equals:
- A
  $4r$
- B
  $2r$
- C
  $2\sqrt2 r$
- D
  $\sqrt3 r$

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Solid State formulas

Solid State, every formula

Density of a unit cell

Atoms in simple cubic

Atoms in BCC

Atoms in FCC

Edge–radius (simple cubic)

Edge–radius (BCC)

Edge–radius (FCC)

Packing efficiency (SC)

Packing efficiency (BCC)

Packing efficiency (FCC/HCP)

Coordination number (SC)

Coordination number (BCC)

Coordination number (FCC)

Octahedral voids

Tetrahedral voids

Radius ratio (octahedral)

Radius ratio (tetrahedral)

Bragg's law

Number of atoms per unit volume

Frenkel defect

Schottky defect

Body diagonal (BCC)

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