Model the effective potential seen by the least bound proton in the nucleus as a square well with depth Bn inside the nuclear radius R, plus a repulsive Coulomb potential from a uniform charge distribution of the other protons inside the nucleus. Estimate Br for 209 Bi (mass number A = 209 and atomic number Z = 83), the largest stable isotope. How is Bn related to the depth of the nuclear potential Vo? Hint: The electrostatic potential a distance r from the center of a uniformly charged sphere of radius R and total charge Q is given by: for r < R. Q V = (3R² — r²) 8πTEOR³
Model the effective potential seen by the least bound proton in the nucleus as a square well with depth Bn inside the nuclear radius R, plus a repulsive Coulomb potential from a uniform charge distribution of the other protons inside the nucleus. Estimate Br for 209 Bi (mass number A = 209 and atomic number Z = 83), the largest stable isotope. How is Bn related to the depth of the nuclear potential Vo? Hint: The electrostatic potential a distance r from the center of a uniformly charged sphere of radius R and total charge Q is given by: for r < R. Q V = (3R² — r²) 8πTEOR³
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![Model the effective potential seen by the least bound proton in the nucleus as a square well with
depth Bn inside the nuclear radius R, plus a repulsive Coulomb potential from a uniform charge
distribution of the other protons inside the nucleus. Estimate Br for 209 Bi (mass number A = 209
and atomic number Z = 83), the largest stable isotope. How is Bn related to the depth of the
nuclear potential Vo?
Hint: The electrostatic potential a distance r from the center of a uniformly charged sphere of
radius R and total charge Q is given by:
for r < R.
Q
V =
(3R² — r²)
8πTEOR³](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1e0d7c53-2a6a-4427-9afd-7aa86bbfce59%2Ffa3ca151-b3c9-4e24-9257-9063d18bd820%2F1yhffw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Model the effective potential seen by the least bound proton in the nucleus as a square well with
depth Bn inside the nuclear radius R, plus a repulsive Coulomb potential from a uniform charge
distribution of the other protons inside the nucleus. Estimate Br for 209 Bi (mass number A = 209
and atomic number Z = 83), the largest stable isotope. How is Bn related to the depth of the
nuclear potential Vo?
Hint: The electrostatic potential a distance r from the center of a uniformly charged sphere of
radius R and total charge Q is given by:
for r < R.
Q
V =
(3R² — r²)
8πTEOR³
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