Problem 1. [35%] A hydrogen atom (with the Bohr radius of 5×10-11 m) is situated

Question

Problem 1. [35%] A hydrogen atom (with the Bohr radius of 5×10-11 m) is situated between two metal plates 0.5 mm apart, which are connected to opposite terminals of a 200 V battery. [The polarizability of a hydrogen atom =0.667 ]

(a) Find the value of the electric field between the plates

(b)Find the dipole moment of the hydrogen atom induced by the electric field, obtained in part (a)

(c) By using the result for the dipole moment, calculate the estimated separation distance d between the electron and nucleus

(d)Estimate the voltage needed to ionize the atom.

Explanation / Answer

a] Electric field between the plates will be:

|E| = V/L = 200/0.5 x 10-3 = 4 x 105 V/m

b] Induced Dipole Moment of the hydrogen atom will be:

p = polarizability x Electric field strength

Subtitute the values of polarizability and Electric field strength to get Dipole Moment.

c] Dipole moment is the product of neighbouring charges and the distance separating them.

So,

p = ed

where d is the separation distance d between the electron (charge -e) and nucleus (charge +e).

use this to determine d.

d] Use d = Bohr radius and use it determine the induced dipole moment needed. Use that to find electric field strength required (thereby giiving the voltage needed).

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