A fuel cell, specifically using hydrogen and oxygen, has found applications in spaceships due to its capability to provide electricity in a lightweight, efficient form. It does not use aluminum as a catalyst but rather commonly uses platinum or other noble metals. Fuel cells operate in an eco-friendly manner, emitting only water as a by-product. Furthermore, they can be categorized as galvanic cells since they convert chemical energy directly into electrical energy.


Which one of the following graphs accurately represents the plot of partial pressure of CS₂ vs its mole fraction in a mixture of acetone and CS₂ at constant temperature?

Let \( \alpha = \dfrac{-1 + i\sqrt{3}}{2} \) and \( \beta = \dfrac{-1 - i\sqrt{3}}{2} \), where \( i = \sqrt{-1} \). If
\[ (7 - 7\alpha + 9\beta)^{20} + (9 + 7\alpha - 7\beta)^{20} + (-7 + 9\alpha + 7\beta)^{20} + (14 + 7\alpha + 7\beta)^{20} = m^{10}, \] then the value of \( m \) is ___________.