Calculating Energies of Pion - Seeming trouble with constants?

In summary, the problem asks to calculate the energy for a 1S->2P transition in lithium and carbon using the energy and eigenvalue equations. Using the given constants of mass, speed of light, atomic number, and fine structure constant, the attempted solutions were significantly incorrect. Further attempts with different values for quantum numbers also failed.
  • #1
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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  • #2
Trying n=2; l=1 also fails. Any ideas?
 

1. What is the purpose of calculating energies of pions?

The purpose of calculating energies of pions is to understand their behavior and properties in different situations. This information can be used to study nuclear interactions, particle physics, and cosmology.

2. What are the constants involved in calculating energies of pions?

The main constants involved in calculating energies of pions are the speed of light (c), Planck's constant (h), and the mass of the pion (m). Other constants such as the fine structure constant (α) and the electron charge (e) may also be used in some calculations.

3. How do I calculate the energy of a pion?

The energy of a pion can be calculated using the equation E = √(p²c² + m²c⁴), where p is the momentum of the pion and m is its mass. The momentum can be calculated using the equation p = γmv, where γ is the Lorentz factor and v is the velocity of the pion.

4. What units are used for energies of pions?

Energies of pions are typically measured in electron volts (eV) or mega electron volts (MeV). These units are commonly used in particle physics and nuclear physics.

5. Why am I having trouble with constants in my calculations?

Trouble with constants in calculations can occur due to incorrect values or units being used, as well as errors in the equations or calculations themselves. It is important to double check all values and equations to ensure accuracy in your calculations.

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