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•• Consider a hypothetical element that forms a solid with bands as shown in Fig. 13.42. (a) Suppose that the isolated atom has configuration 1s²2s². If its equilibrium separation is ro = a, is the solid a con- ductor or an insulator? What if ro = b? Answer both questions for the case that the atomic configuration is (b) 1s²2s²2p' and (c) 1s²2s²2p°. 3s 2p 2s 1s b. a

•• Consider a hypothetical element that forms a solid with bands as shown in Fig. 13.42. (a) Suppose that the isolated atom has configuration 1s²2s². If its equilibrium separation is ro = a, is the solid a con- ductor or an insulator? What if ro = b? Answer both questions for the case that the atomic configuration is (b) 1s²2s²2p' and (c) 1s²2s²2p°. 3s 2p 2s 1s b. a

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Consider a hypothetical element that forms a solid with bands as shown in the Figure. A. Suppose that the isolated atom has configuration 1s22s2. If its equilibrium separation is r0= a, is the solid a conductor or an insulator? What if r0= b? Answer both questions for the case that the atomic configuration is B. 1s22s22p1 and C. 1s22s22p6.

## Consider a Hypothetical Element and Band Formation **Problem 13.34:** Consider a hypothetical element that forms a solid with energy bands as represented in Fig. 13.42: - **(a)** Suppose the isolated atom has the electron configuration \(1s^22s^2\). If its equilibrium separation is \(r_0 = a\), is the solid a conductor or an insulator? What if \(r_0 = b\)? - Answer both questions for the cases when the atomic configuration is: - **(b)** \(1s^22s^22p^1\) - **(c)** \(1s^22s^22p^6\) ### Explanation of Fig. 13.42: - The graph shows the energy bands formed by the overlapping atomic orbitals \(1s\), \(2s\), \(2p\), and \(3s\) over a separation distance \(r\). - **Horizontal Axis (r):** Represents the distance between atoms in the solid. - **Vertical Bands:** - **1s Band:** This is depicted as a narrow band at the bottom, indicating lower energy levels. - **2s and 2p Bands:** Wider bands that overlap as the distance \(r\) decreases, indicating possible conductivity when overlaps occur. - **3s Band:** The widest and most spread band, suggesting higher energy availability and greater overlap potential at smaller distances. - **Dashed Lines \(a\) and \(b\):** These represent specific values of the equilibrium separation \(r_0\): - **At \(r_0 = a\):** Assess overlap to determine if the solid is a conductor (bands overlap) or an insulator (bands do not overlap). - **At \(r_0 = b\):** Re-evaluate overlap for conductor or insulator properties. This setup helps in analyzing electronic properties by observing band overlaps and identifying potential conductive behavior in the hypothetical solid.
Transcribed Image Text:## Consider a Hypothetical Element and Band Formation **Problem 13.34:** Consider a hypothetical element that forms a solid with energy bands as represented in Fig. 13.42: - **(a)** Suppose the isolated atom has the electron configuration \(1s^22s^2\). If its equilibrium separation is \(r_0 = a\), is the solid a conductor or an insulator? What if \(r_0 = b\)? - Answer both questions for the cases when the atomic configuration is: - **(b)** \(1s^22s^22p^1\) - **(c)** \(1s^22s^22p^6\) ### Explanation of Fig. 13.42: - The graph shows the energy bands formed by the overlapping atomic orbitals \(1s\), \(2s\), \(2p\), and \(3s\) over a separation distance \(r\). - **Horizontal Axis (r):** Represents the distance between atoms in the solid. - **Vertical Bands:** - **1s Band:** This is depicted as a narrow band at the bottom, indicating lower energy levels. - **2s and 2p Bands:** Wider bands that overlap as the distance \(r\) decreases, indicating possible conductivity when overlaps occur. - **3s Band:** The widest and most spread band, suggesting higher energy availability and greater overlap potential at smaller distances. - **Dashed Lines \(a\) and \(b\):** These represent specific values of the equilibrium separation \(r_0\): - **At \(r_0 = a\):** Assess overlap to determine if the solid is a conductor (bands overlap) or an insulator (bands do not overlap). - **At \(r_0 = b\):** Re-evaluate overlap for conductor or insulator properties. This setup helps in analyzing electronic properties by observing band overlaps and identifying potential conductive behavior in the hypothetical solid.
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