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
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Chapter2: Second-order Linear Odes
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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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