The hydrogen molecular ion H^1_2, with one electron and two protons, is the simp
ID: 1549707 • Letter: T
Question
The hydrogen molecular ion H^1_2, with one electron and two protons, is the simplest molecule. The equilibrium spacing between the protons is 0.11 nm. Suppose the electron is at the midpoint between the protons and moving at 1.5 times 10^6 m/s perpendicular to a line between the protons. How far (in nm) does the electron move before reaching a turning point? Because of their larger mass, the protons remain fixed during this interval of time. Note, that an accurate description of H^1_2 requires quantum mechanics. Even so, a classical calculation like this provides some insight into the molecule. Express your answer using two significant figures.Explanation / Answer
Given
P-----e-----P
electron moving with velocity v = 1.5*10^6 m/s perpendicular to line between the protons
separation of protons is = 0.11 nm
the potential of the electron due to two protons is V = 2kq/r
which is equal to the electric potential energy per unit charge
2kq/r = U/q
U = 2kq^2/r
and due to conservation of energy which is again equal to the kinetic energy of the electron
2kq^2/r = 0.5*mv^2
r = 4kq^2/mv^2
r = (4*9*10^9(1.6*10^-19)^2) /(9.10938*10^-31*(1.5*10^6)^2)m
r = 4.4964641*10^-10 m
r = 0.44964641 nm
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.