24. C.

Notice that quadrilateral $E J C I$ is a rhombus. Let's assume the edge length of the cube is $s$. Then
$$
\begin{array}{l}
E C=\sqrt{3} s, J I=\sqrt{2} s . \\
\text { Hence } S_{\text {rhombusEJCI }}=\frac{1}{2} E C \cdot J I=\frac{\sqrt{6}}{2} s^{2} \\
\Rightarrow R=\frac{\sqrt{6}}{2} \Rightarrow R^{2}=\frac{3}{2} .
\end{array}
$$
24. As shown in Figure 7, in the cube $A B C D-E F G H$, $J$ and $I$ are the midpoints of edges $F B$ and $H D$, respectively. Let $R$ be the ratio of the area of the section $E J C I$ to the area of one face of the cube. Then the value of $R^{2}$ is ( ).
(A) $\frac{5}{4}$
(B) $\frac{4}{3}$
(C) $\frac{3}{2}$
(D) $\frac{25}{16}$
(E) $\frac{9}{4}$