 Home

Codex Wiki

List of universities

University of Cambridge

Course of the University of Cambridge

Natural sciences course of the University of Cambridge

Year of the natural sciences course of the University of Cambridge

Year 2 of the natural sciences course of the University of Cambridge

Chemistry A course of the University of Cambridge

Past exam of the chemistry A course of the University of Cambridge

2022

Paper 2

Write $t_s=|\beta_s|$ and $t_p=|\beta_p|$, so
$$
E_s=\alpha_s-2t_s\cos(ka),\qquad
E_p=\alpha_p+2t_p\cos(ka).
$$
The labelled key points of the two <dispersion relations> are
$$
\begin{array}{c|c|c}
k&E_s&E_p\\\hline
0&\alpha_s-2t_s&\alpha_p+2t_p\\
\pi/(2a)&\alpha_s&\alpha_p\\
\pi/a&\alpha_s+2t_s&\alpha_p-2t_p
\end{array}
$$
The $s$ band rises from centre to boundary and the axial $p$ band falls. The separated-band assumption requires $\alpha_p-\alpha_s>2(t_s+t_p)$. The upper-left panel shows a representative pair, with the other panels supplying the requested comparisons in part (b).

\Image[/past-exam-of-the-chemistry-a-course-of-the-university-of-cambridge/2022/paper-2-sp-bands.png]
{title=Original one-dimensional s and axial-p band sketches, comparing separated bands, mixing, and the equal-on-site-energy special case}

Solution

Past exam of the chemistry A course of the University of Cambridge / 2022 / Paper 2 / A9 / a / ii / Solution

Past exam of the chemistry A course of the University of Cambridge / 2022 / Paper 2 / A9 / a / ii / Solution

 Ancestors (14)

 Discussion (0)

 Articles by others on the same topic (0)

Past exam of the chemistry A course of the University of Cambridge / 2022 / Paper 2 / A9 / a / ii / Solution

 Ancestors (14)

 Discussion (0)  Subscribe (1)

 Articles by others on the same topic (0)

 Discussion (0)