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Stable molecules form when atoms arrange in a way to exert equal force on each other. One such molecule is phosphate, PO³-, which forms a tetrahedron shape. The notation indicates 4 oxygen atoms with a single phosphorus atom (and an overall excess of 3 electrons). Consider a coordinate system where the four oxygen atoms that form the tetrahedron are placed at (1, 0, 0), (0, 1, 0), (0, 0, 1), and (−1/3, -1/3, -1/3). (a) To have equal forces the phosphate atom must be placed equidistant from each of the oxygen atoms. Assume the phosphorus atom has the same value for all coordinates, i.e. it is located at (a, a, a). Find a. (b) Determine the bond angle, that is the angle between the lines that join the phosphorus atom to two of the oxygen atoms. Estimate it in degrees.

Stable molecules form when atoms arrange in a way to exert equal force on each other. One such molecule is phosphate, PO³-, which forms a tetrahedron shape. The notation indicates 4 oxygen atoms with a single phosphorus atom (and an overall excess of 3 electrons). Consider a coordinate system where the four oxygen atoms that form the tetrahedron are placed at (1, 0, 0), (0, 1, 0), (0, 0, 1), and (−1/3, -1/3, -1/3). (a) To have equal forces the phosphate atom must be placed equidistant from each of the oxygen atoms. Assume the phosphorus atom has the same value for all coordinates, i.e. it is located at (a, a, a). Find a. (b) Determine the bond angle, that is the angle between the lines that join the phosphorus atom to two of the oxygen atoms. Estimate it in degrees.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Stable molecules form when atoms arrange in a way to exert equal force on each other. One such molecule is phosphate, PO³-, which forms a tetrahedron shape. The notation indicates 4 oxygen atoms with a single phosphorus atom (and an overall excess of 3 electrons). Consider a coordinate system where the four oxygen atoms that form the tetrahedron are placed at (1, 0, 0), (0, 1, 0), (0, 0, 1), and (−1/3, -1/3, -1/3). (a) To have equal forces the phosphate atom must be placed equidistant from each of the oxygen atoms. Assume the phosphorus atom has the same value for all coordinates, i.e. it is located at (a, a, a). Find a. (b) Determine the bond angle, that is the angle between the lines that join the phosphorus atom to two of the oxygen atoms. Estimate it in degrees.
Transcribed Image Text:Stable molecules form when atoms arrange in a way to exert equal force on each other. One such molecule is phosphate, PO³-, which forms a tetrahedron shape. The notation indicates 4 oxygen atoms with a single phosphorus atom (and an overall excess of 3 electrons). Consider a coordinate system where the four oxygen atoms that form the tetrahedron are placed at (1, 0, 0), (0, 1, 0), (0, 0, 1), and (−1/3, -1/3, -1/3). (a) To have equal forces the phosphate atom must be placed equidistant from each of the oxygen atoms. Assume the phosphorus atom has the same value for all coordinates, i.e. it is located at (a, a, a). Find a. (b) Determine the bond angle, that is the angle between the lines that join the phosphorus atom to two of the oxygen atoms. Estimate it in degrees.
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