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Chapter 4: Q22-51P (page 749)

Using Thomson鈥檚 (outdated) model of the atom described in Problem 22.50, consider an atom consisting of two electrons, each of charge -e, embedded in a sphere of charge +2e and radius R. In equilibrium, each electron is a distance d from the center of the atom (Fig. P22.51). Find the distance d in terms of the other properties of the atom.

Short Answer

Expert verified

The distance of each atom from the center of sphere is \(\frac{R}{2}\).

Step by step solution

01

Identification of given data

The charge of the sphere is\(Q = 2e\)

The charge of each atom in sphere is\(q = - e\)

The radius of sphere is\(R\)

The distance from the centre for each atom is \(d\)

02

Conceptual Explanation

The distance of each atom in sphere is calculated by equating the force on each atom by the charge of sphere.

03

Determination of distance of each atom from the center of sphere

The distance of each atom from center of sphere is given below:

\(\begin{aligned}\frac{{kQq}}{{{R^2}}} &= \frac{{kQq}}{{{{\left( {d + d} \right)}^2}}}\\2d &= R\\d &= \frac{R}{2}\end{aligned}\)

Therefore, the distance of each atom from the center of sphere is \(\frac{R}{2}\).

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