Answer:


When a one-dimensional crystal with a lattice dimension 'a' is distorted to have a lattice dimension of '2a', it can have an impact on its electronic structure. In this scenario, the potential outcomes can be categorized into four options: (a) the electronic structure remains unchanged, (b) the width of the conduction band decreases and a band gap is generated, (c) the width of the conduction band increases, or (d) the width of the conduction band remains unchanged.




If the electronic structure of the crystal remains unaffected by the distortion, it implies that the energy bands and their characteristics, such as the width of the conduction band and the presence or absence of a band gap, remain the same. However, such a scenario is highly unlikely as any distortion in the lattice dimension would inevitably cause changes in the electronic structure.


When the lattice dimension is enhanced to '2a', the increase in the interatomic distance affects the electronic interactions within the crystal. This alteration can lead to a decrease in the width of the conduction band and the formation of a band gap. As a result, the crystal, which was originally metallic, now becomes a semiconductor or an insulator. This phenomenon is commonly observed in the case of one-dimensional crystals.


In certain cases, the distortion of the lattice dimension can cause an increase in the width of the conduction band. This can occur when the electronic interactions between neighboring atoms become stronger due to the change in lattice dimension. Consequently, the crystal may exhibit enhanced metallic behavior with a wider conduction band.


It is highly improbable for the width of the conduction band to remain the same when the lattice dimension is altered. Any change in the lattice dimension would inevitably affect the electronic interactions and, consequently, alter the width of the conduction band.


Based on the possible outcomes, it is most likely that the width of the conduction band decreases and a band gap is generated when a one-dimensional crystal with a lattice dimension 'a' is distorted to have a lattice dimension of '2a'. This transformation changes the crystal from being metallic to a semiconductor or an insulator. Nonetheless, it is essential to consider the specific characteristics and conditions of the crystal structure to determine the precise impact of the lattice distortion on its electronic structure.