Purchase Solution

Accuracy of First Order Theory

Not what you're looking for?

Ask Custom Question

Problem 20: The finite size of the proton perturbs the energy of the n = 1 orbit in a hydrogen atom.

(i) Given the proton to be a uniformly charge sphere of radius R = 1 fm, determine the first order energy shift, making reasonable approximations. How accurate should the first order theory be in this case?

(ii) Do the calculation again for the hypothesis that the nuclear charge is uniformly distributed over the surface of a spherical shell of radius R.

(iii) Once again do the calculations for a muon (mass = 106 MeV/c2) in orbit around Pb nucleus (Z = 82, A = 207) with uniform and spherical-shell charge density distributions. Assume the nuclear radius scales like R ~ A1/3. How accurate should the first order theory be in this case?

Purchase this Solution
Solution Summary

The solution is attached in two files. The files are identical in content, only differ in format. The first is in MS Word XP Format, while the other is in Adobe .pdf format. Therefore, you can choose the format that is most suitable to you. Hope this helps.

Solution Preview

The potential energy outside the nucleus is:
U(r) = - kq^2/r r > r_0

Were k is the Coloumb constant.

The charge inside the sphere as a ...

Purchase this Solution
Free BrainMass Quizzes
Classical Mechanics

This quiz is designed to test and improve your knowledge on Classical Mechanics.

The Moon

Test your knowledge of moon phases and movement.

Basic Physics

This quiz will test your knowledge about basic Physics.

Introduction to Nanotechnology/Nanomaterials

This quiz is for any area of science. Test yourself to see what knowledge of nanotechnology you have. This content will also make you familiar with basic concepts of nanotechnology.

Variables in Science Experiments

How well do you understand variables? Test your knowledge of independent (manipulated), dependent (responding), and controlled variables with this 10 question quiz.

View More Free Quizzes
Related BrainMass Solutions

  • Motivation Theories and Scenarios

    Goal-Setting theory- accuracy goal, also may be extrinsic motivation The principles of this theory are: Clear (not vague) and understandable, so we know what to do and what not to do. Challenging, so we will be stimulated and not be bored.

  • Goal Theory of Motivation

    The underlying findings of the goal theory of motivation is that in order to direct ourselves we set ourselves goals that are: · Clear (not vague) and understandable, so we know what to do and what not to do.

  • Insider trading issues for Reliant Electric's takeover

    Definitely, his disclosure of said information to his uncle violates this theory 4. Under the Sarbanes-Oxley Act of 2002, who would be required to certify the accuracy of financial statements filed with the SEC?

  • Perturbation theory

    8420 Perturbation Theory Equation Find the real roots of the equation x^5 + ex-1=0 approximately to O(e^2) usind perturbation theory.

  • Improved Euler method with Butcher Tableau

    a〗_1r ⋮ ⋮ ⋮ c_r a_r1 ...〖 a〗_rr b_1 ...b_r To guarantee at least first order accuracy, and in addition consistency, we require the following two conditions: (1) ∑_(j=1)^r▒〖a_ij=c_i, i=1,2,...r〗 (2) ∑_(j=1)^r▒〖b_j=1〗 If (1)

  • John Rawls Principles of Justice & Nozick's View of Libertarianism

    According to Donaldson & Preston (1995), the stakeholder theory has been advanced and justified in the management text on the basis of its descriptive accuracy, instrumental power, and normative validity: Descriptive accuracy?

  • Communication Models

    First, the theory is concerned with the "effect of mutual interaction between people", and less with the actual lines of communication.

  • Healthcare Organization

    We will first take up the bureaucracy theory followed by the classical and the power politics theory.// Weber's Bureaucracy Theory The Bureaucracy theory was proposed by German sociologist Max Weber.

  • Feedback Loops- Industrial Services of America

    The anonymity of these reports is protected through strict corporate guidelines, (ISA, nd). The report then motivates some change from the Audit Committee, or Executive Board in order to close the gap in information accuracy.

View More Related Solutions