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Transcribed Image Text:Liquid water has a large dielectric constant of ɛ, = 80. Suppose that a single sodium ion (Na+,
carrying a positive charge of +1e) is held in the middle of a beaker of pure water. Compared to
the volume of the sodium ion, the volume of the water can be effectively treated as infinite.
a) Write down the electric displacement at r distance away from the sodium ion.
b) Write down the electric field at r distance away from the sodium ion.
c) Write down the electrostatic force that the sodium ion acts on a water molecule that is 2nm
away from the ion and oriented with its dipole moment radially away from the ion.
d) Calculate the polarization at a distance r = 2nm away from the sodium ion.
e) The dipole moment of a water molecule is 6.17 x 10-30C · m. Estimate how much fraction
of the water molecules that are at 2nm away from the sodium ion are reoriented by the
sodium ion. (Assume that there are only two possible states for these water molecules:
either randomly oriented and showing zero macroscopic polarization, or reoriented by the
sodium ion and with its dipole moment aligned with the electric field.) (Hint: 18g of water
has a volume of 18cm³, and contains 6.02 x 1023 water molecules)
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