Chapter 4: Q12E (page 746)

Electric Fields in an Atom. The nuclei of large atoms, such as uranium, with 92 protons, can be modeled as spherically symmetric spheres of charge. The radius of the uranium nucleus is approximately $7.4 \times 10^{- 15} m$ . (a) What is the electric field this nucleus produces just outside its surface? (b) What magnitude of electric field does it produce at the distance of the electrons, which is about $1.0 \times 10^{- 10} m$ ? (c) The electrons can be modeled as forming a uniform shell of negative charge. What net electric field do they produce at the location of the nucleus?

Short Answer

Expert verified

(a) The electric field this nucleus produces just outside its surface is $2.42 \times 10^{21} N / C$ .

(b) The magnitude of electric field is $1.3 \times 10^{13} N / C$ .

Step by step solution

Definition of Electric field

The term electric field may be defined as the area around the charge where a positive test charge experienced a force.

Determine the electric field

The electric field can be calculated by the relation $E = \frac{q_{enq}}{4 {ττε}_{0} r^{2}}$

(a) For $r_{n}$ the electric field is

$E = \frac{q_{enq}}{4 {ττε}_{0} r^{2}} E = \frac{9 \times 10^{9} (92 \times 1.6 \times 10^{- 19})}{{(7.4 \times 10^{- 15})}^{2}} E = 2.42 \times 10^{21} N / C$

Hence,the electric field this nucleus produces just outside its surface is $2.42 \times 10^{21} N / C$ .

For $r_{1}$ the electric field is

$E = \frac{q_{enq}}{4 {ττε}_{0} r_{1}^{2}}$

$E = \frac{9 \times 10^{9} (92 \times 1.6 \times 10^{- 19})}{{(1.0 \times 10^{- 10})}^{2}} E = 1.3 \times 10^{13} N / C$

Hence,the magnitude of electric field is $1.3 \times 10^{13} N / C$ .

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Definition of Electric field

Determine the electric field

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