Example: Suppose that the data from X-ray diffraction of a crystal indicates that the positions of the atoms in a molecule are as follows: The position of the carbon atom is C = 0f + 0f + Ok, the position of a neighboring oxygen atom is ö = 2î + 2j + k, and a hydrogen atom is located at H = -î + 2j – k. The oxygen atom and the hydrogen atoms are both bonded to the carbon atom. Distances are in nanometers (nm). a. What is the length ||0|| of the C-O bond? b. What is the length ||Ħ|| of the C-H bond? c. What is the angle 0 between the C-O and C-H bonds? You can solve this problem by taking the two ways to find the scalar product and setting them equal to each
Example: Suppose that the data from X-ray diffraction of a crystal indicates that the positions of the atoms in a molecule are as follows: The position of the carbon atom is C = 0f + 0f + Ok, the position of a neighboring oxygen atom is ö = 2î + 2j + k, and a hydrogen atom is located at H = -î + 2j – k. The oxygen atom and the hydrogen atoms are both bonded to the carbon atom. Distances are in nanometers (nm). a. What is the length ||0|| of the C-O bond? b. What is the length ||Ħ|| of the C-H bond? c. What is the angle 0 between the C-O and C-H bonds? You can solve this problem by taking the two ways to find the scalar product and setting them equal to each
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Transcribed Image Text:(4) The scalar product is also useful for applications other than finding the work done by a force. The scalar product
makes some problems that would otherwise be difficult relatively easy.
Example: Suppose that the data from X-ray diffraction of a crystal indicates that the positions of the atoms in a
molecule are as follows: The position of the carbon atom is C = 0i + 0f + 0k, the position of a neighboring oxygen
atom is ö = 2î + 2j + k, and a hydrogen atom is located at H = -î + 2î – k. The oxygen atom and the hydrogen
atoms are both bonded to the carbon atom. Distances are in nanometers (nm).
a. What is the length ||Ō|| of the C-O bond?
b. What is the length ||H|| of the C-H bond?
c. What is the angle 0 between the C-0 and C-H bonds?
You can solve this problem by taking the two ways to find the scalar product and setting them equal to each
other, i.e., use the fact that 0 H = OH cos 0 = 0,Hx + 0,Hy+ 0,Hz.
Expert Solution
Step 1
The position vectors of the carbon, oxygen and hydrogen atoms are given to be
As can be seen from the position vector of carbon atom, it is located at the origin of the system, and the hydrogen and oxygen atom are attached via bonds to the carbon atom.
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