I need to analyze Camara Laye’s The Radiance of the King from a post-structuralist perspective, but before doing that, I also need to demonstrate...

The question seems to have two different unrelated parts, one having to do with a novel and one concerning the nature of post-structuralism. 

First, post-structuralism is a general rubric covering many specific types of theory, including theories about gender, language, and political and social structures. It is rarely applied to the sciences as its main focus is on social construction of understanding. Where it would apply to science is not so much in judging whether a theory is accurate but in looking at how our assumptions influence the way we approach science. For that reason, evaluating the big bang theory may not be the best way to demonstrate an understanding of post-structuralist thinking. If you're interested in considering something scientific, I'd recommend looking at something in the realm of science that has a strong social component so you can think about the assumptions people bring to bear on scientific concepts.

A good area to discuss might be something like our understanding of menopause. On a scientific level, menopause consists of a biological process that is undergone by most women of the world in their 50s. While the physical changes are simply matters of fact, how we view them is socially constructed. For example,  in some countries menopause is treated almost as a disease, and women going through in the twentieth century in the rich world often prescribed hormone replacement therapy to maintain high levels of estrogen. A post-structuralist analysis would look at social construction of menopause by first deconstructing the binary association of youth with very positive terms (why should saying someone looks "young" be a compliment? why is "youthful" used as a positive term?) and aging with negative terms (think about how we associate age with "old-fashioned", "narrow-minded", lacking energy, unattractive). Next, we might think of the social factors that lead some people to think of menopause as a disease and others to think of it simply as a natural process. Even more interesting, different cultures not only think of menopause differently but women of different cultures going through precisely the same physical process report different symptoms (reference below). In other words, some of what we think of as a medical understanding of "menopause" turns out to be culturally determined.  Thus this would be a good example of how post-structuralism, by making us aware of cultural perspectives, can contribute to more rigorous scientific thinking, by making us examine evidence from outside particular cultural bubbles. 

In thinking about Camara Laye’s The Radiance of the King, you should focus on using postcolonial theory to see Clarence as the emblem of someone who thinks of Africa in terms of white privilege. You should also discuss how what once were considered "natural" qualities of Europeans vs. Africans and men vs. women are shown as culturally determined by some of the role reversals in the novel. 

Clarence automatically sees his interactions through a lens of white entitlement and power, despite the reality of the novel being precisely the opposite, with the African characters holding power. You should discuss how Clarence's European point of view means that he does not even see that he has, in a sense, become a slave who exists mainly to breed mixed-race children, reversing the traditional binary of Europeans as masters and blacks as slaves. You should also look at the binary of masculinity equaling power and femininity weakness as being disrupted by Clarence's masculinity being treated as a passive reproductive ability.