The hydrogen molecular ion H, with one electron and two protons, is the simplest
ID: 2166776 • Letter: T
Question
The hydrogen molecular ion H, with one electron and two protons, is the simplest molecule. The equilibrium spacing between the protons is 0.11nm . Suppose the electron is at the midpoint between the protons and moving at 1.5*10^6m/s perpendicular to a line between the protons.How far (in nm) does the electron move before reaching a turning point? <-----question
Because of their larger mass, the protons remain fixed during this interval of time. Note, that an accurate description of H requires quantum mechanics. Even so, a classical calculation like this provides some insight into the molecule.
Explanation / Answer
Let 2x be the horizontal spacing between the protons (.11 nm). Let y be the vertical distance above this horizontal line of the oscillating electron. The total energy of the electron will then be its PE with each proton plus its KE ; E = - 2kq^2/SqRt(x^2+y^2) + (1/2)mv^2 You are given "v" when y=0 , so you can calculate "E" This "E" will be constant so you can now use it back in the original formula to calculate "y" when v=0 , the turning point.
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