Problem 2: An early model of the atom, proposed by Rutherford after his discovery of the atomic nucleus, had a positive point charge +Ze (the nu- cleus) at the center of a sphere of radius R with uniformly distributed neg- ative charge -Ze. Z is the atomic number, the number of protons in the nucleus and the number of electrons in the negative sphere. Show that the electric field strength inside this atom is Ein = Ze 47€ 1 r² R³ a) Fig.2 illustrates the model of the atom. In the figure, draw the Gaussian surface that you will use to find the field. Draw the vectors that represent the electric field at the Gaussian surface. How do you know the direction of the electric field inside the atom? qize R S- FIG. 2: The scheme for Prob- lem 2

University Physics Volume 2
18th Edition
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Chapter5: Electric Charges And Fields
Section: Chapter Questions
Problem 67P: Consider an electron that is 1010 m from an alpha particle (q=3.21019C) . (a) What is the electric...
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I tried this problem and I asked my professor about it and he tells me I got all of the answers wrong and I don't know why I keep getting the wrong answer. Can you help me with Part A,B, AND C and can you label which part is A,B, and C

Problem 2: An early model of the atom, proposed by Rutherford after his
discovery of the atomic nucleus, had a positive point charge +Ze (the nu-
cleus) at the center of a sphere of radius R with uniformly distributed neg-
ative charge -Ze. Z is the atomic number, the number of protons in the
nucleus and the number of electrons in the negative sphere. Show that the
electric field strength inside this atom is
Ein =
Ze 1
r
Απερ r² R³
a) Fig.2 illustrates the model of the atom. In the figure, draw the Gaussian
surface that you will use to find the field. Draw the vectors that represent
the electric field at the Gaussian surface. How do you know the direction of
the electric field inside the atom?
q=ze
R
70
S-
FIG. 2: The scheme for Prob-
lem 2
c) A uranium atom has Z = 92 and R = 0.10 nm. What is the electric field strength at r = R/2?
b) What is the volume charge density p. of the negative sphere? Use Gauss's law and the symmetry
arguments in order to find the expression for the electric field strength inside the atom. What is the electric
field strength outside this atom?
Transcribed Image Text:Problem 2: An early model of the atom, proposed by Rutherford after his discovery of the atomic nucleus, had a positive point charge +Ze (the nu- cleus) at the center of a sphere of radius R with uniformly distributed neg- ative charge -Ze. Z is the atomic number, the number of protons in the nucleus and the number of electrons in the negative sphere. Show that the electric field strength inside this atom is Ein = Ze 1 r Απερ r² R³ a) Fig.2 illustrates the model of the atom. In the figure, draw the Gaussian surface that you will use to find the field. Draw the vectors that represent the electric field at the Gaussian surface. How do you know the direction of the electric field inside the atom? q=ze R 70 S- FIG. 2: The scheme for Prob- lem 2 c) A uranium atom has Z = 92 and R = 0.10 nm. What is the electric field strength at r = R/2? b) What is the volume charge density p. of the negative sphere? Use Gauss's law and the symmetry arguments in order to find the expression for the electric field strength inside the atom. What is the electric field strength outside this atom?
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