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Q. 55

Expert-verified
Found in: Page 685

Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

Book edition 4th
Author(s) Randall D. Knight
Pages 1240 pages
ISBN 9780133942651

An early model of the atom, proposed by Rutherford after his discovery of the atomic nucleus, had a positive point charge +Ze (the nucleus) at the center of a sphere of radius R with uniformly distributed negative charge -Ze. Z is the atomic number, the number of protons in the nucleus and the number of electrons in the negative sphere. a. Show that the electric field strength inside this atom is b. What is E at the surface of the atom? Is this the expected value? Explain. c. A uranium atom has Z = 92 and R = 0.10 nm. What is the electric field strength at r = 1 2 R?

It has been verified that the electric field strength inside the atom is

the electrical field is 0 at any surface of any atom

The electric field strength of uranium at r=R / 2 is

See the step by step solution

part (a) step 1: given  information

We use Gauss' Law to find the electric field inside the sphere.

Where

is the Electric Flux

E is the Electric Field

d a is the Area

Q is the Total Charge

0 is the Permittivity

The charge inside the sphere from the electron can be evaluated as:

The total charge enclosed in a sphere of radius r is

r is the radius inside the atom.

The electric field from the electrons can thus be given by:

The electric field from nucleus is from a point charge Z e It is thus being given by:

Combining the above equations, we get:

part (b) step 1: given  information

Since atoms are neutral therefore it can be said that the electric field strength at the surface of the atom is 0

part (c) step 1: given  information

The electric field strength at the uranium surface is calculated as

Calculation:

Evaluating electric field for the values of

, ,, r=0.5 R