Surface Area of a Molecule

Geometry Level 4

A new molecule \( \ce{A2Z}\) has been discovered. It is made of two atoms of \( \ce{A} \) and one atom of \( \ce{Z}\). The surface area of a molecule can tell us loads about the chemical and physical properties of the molecule, hence it is imperative that we calculate it.

If the surface area of an \(\ce{A2Z}\) molecule is \( S \text{ pm}^2\), then what is \( \dfrac{S}{\pi} \)?

Details and Assumptions

  • We can model the molecule as three overlapping spheres as shown in the animation. The white spheres are atoms of \( \ce{A}\) and the red sphere is an atom of \(\ce{Z}\)

  • The radius of Sphere \( \ce{A}\) is 40 pm

  • The radius of Sphere \( \ce{Z}\) is 60 pm

  • The distance between the centers of Sphere \(\ce{A}\) and Sphere \(\ce{Z}\) is 80 pm


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