Energy bands of a material is decided by : (a) The atomic number Which of the following is correct ?
(b) Relative spacing of atoms in the solids
(c) Melting point of the material
(d) Hardness of the material
(a), (b)
Bands form when isolated atoms are brought close enough for their electron wavefunctions to overlap, so exactly two things matter: which atom, and how far apart.
(a) Atomic number — correct. It fixes the electronic configuration, and therefore which discrete energy levels exist in the first place. The bands of a solid are broadened versions of those atomic levels, so silicon (Z = 14, configuration ending 3s23p2) and germanium (Z = 32, 4s24p2) give different band structures precisely because their outer levels differ.
(b) Relative spacing of atoms — correct, and it is the mechanism. Bring N identical atoms together and the Pauli exclusion principle forbids N electrons from occupying the same level, so each atomic level splits into N closely spaced levels — a band. The amount of splitting depends on the overlap, hence on the interatomic distance:
| Spacing | Overlap | Result |
|---|---|---|
| Very large | None | Sharp atomic levels, no bands |
| Moderate | Partial | Bands separated by a gap — semiconductor or insulator |
| Small | Strong | Bands broaden and overlap — metal |
This is exactly why carbon appears as both diamond (Eg = 5.5 eV, an insulator) and graphite (a conductor): same atomic number, different lattice spacing and arrangement.
(c) Melting point and (d) hardness are consequences, not causes. Both are set by the strength of the interatomic bonding, which is itself determined by the same electronic structure that produces the bands. Diamond is hard because its covalent bonds are strong, and its band gap is wide for the same underlying reason — but neither property decides the other. Correlation is not causation, and the question asks what the bands are decided by.
So (a) and (b) — option 3.
The formal statement is that the band structure \(E(k)\) is obtained by solving Schrodinger's equation for an electron in the periodic potential of the lattice. That potential has exactly two ingredients: the potential of the individual atom, set by Z, and the periodicity, set by the lattice spacing. Nothing else enters the calculation, which is the cleanest way to see why (a) and (b) are the answer.
What follows from the gap is the entire classification of solids: overlapping bands give a metal, a gap of a few eV gives a semiconductor, and a gap beyond about 3 eV gives an insulator — a distinction that changes the room-temperature conductivity by more than twenty orders of magnitude.
Hence, the correct statements are (a) and (b).
Similar Questions
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A. 33
B. 49
C. 31
D. 51
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Codes :
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I. Graphene in its purest and defect free form has electrical conductivity lesser than that of Gold and Copper
II. It is possible to develop graphene in the form of nano-ribbons and quantum dots
Choose the correct option from the list given below.
