Calculating Energies of Pion - Seeming trouble with constants?

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SUMMARY

The discussion focuses on calculating the energy for the 1S->2P transition in lithium and carbon using the formula E = mc^2/sqrt(1+(Za/lambda)^2) and lambda = n + 1/2 + sqrt((l+1/2)^2 - (Za)^2). The user employed constants such as the mass of the pion (139.6 MeV), speed of light (3E8 m/s), atomic number (Z=3), and a = 7.29E-3 from CODATA. Despite these inputs, the results were significantly inaccurate, prompting a request for clarification on the appropriate constants to use for accurate calculations.

PREREQUISITES
  • Understanding of quantum mechanics and atomic transitions
  • Familiarity with the constants used in particle physics, specifically the mass of pions
  • Knowledge of the equations governing energy transitions in quantum systems
  • Basic proficiency in mathematical manipulation of physical equations
NEXT STEPS
  • Research the properties and constants of pions in particle physics
  • Study the derivation and application of the energy transition formulas in quantum mechanics
  • Explore the significance of quantum numbers (n and l) in energy calculations
  • Learn about the CODATA values and their relevance in physics calculations
USEFUL FOR

This discussion is beneficial for physics students, researchers in quantum mechanics, and anyone involved in calculating atomic energy transitions, particularly in the context of pion interactions.

unicornflyers
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Homework Statement



Calculate the energy for 1S->2P transition in lithium and carbon. We had to calculate the energy and eigenvalue equations (though I verified these are correct)

Homework Equations


E = mc^2/sqrt(1+(Za/lambda)^2)
lambda = n + 1/2 + sqrt((l+1/2)^2- (Za)^2)


The Attempt at a Solution



The constants I tried were the mass of the pion =139.6 MeV
c = 3E8
Z =3
a = 7.29E-3 (Via CODATA)
and I'm assuming that n = 1, l =0.

When I plug these in, I get something WAY off. Like not even order of magnitude correct, off. So am I using the right constants? If not, which ones should I be using for these?
 
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Trying n=2; l=1 also fails. Any ideas?
 

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