At an early stage in the development of the atomic theory, J.J. Thompson had pro

Question

At an early stage in the development of the atomic theory, J.J. Thompson had proposed an atom consisting of a positive charge, Ze, where Z is an integer and e is the fundamental unit of charge (1.6 x 10^-19 coulomb), uniformly distributed throughout a sphere of radius a. The electrons, of charge -e, were considered to be point charges embedded in the positive charge.

(a). Find the force acting on once eletron as a function of its distance r from the center of the sphere. Assume that the other charges are uniformly distributed throughout the sphere.

(b). What type of motion does this electron execute?

(c). What is the frequency fro a typical atomic radius of 1 angstrom?

(d). How does this frequency compare with that of the visivle light radiated by atoms?

Explanation / Answer

1) F of the force on an electron when it is a distance r from the centre of a sphere; this is given by Coulomb's law:

F = k (+2e)(Ze)/r^2

where k is the Coulomb constant , r is the dist and (Ze) is the nuclear charge.

2) The motion of electrons around the atom is associated with K.E. If (v) is the average speed of an electron as it spins around the nucleus at a certain average radius (r), its K.E. = ½ Mv^2

3) F = Mv^2 / r
From this we can find v.
Now putting v in Frequency = v / 2*pi*r, we get frequency.

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