Find the wavelengths Kα, Kβ , Lα and Lβ from elemental Cu

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SUMMARY

The discussion focuses on calculating the wavelengths of the characteristic Kα, Kβ, Lα, and Lβ x-rays emitted from elemental copper (Cu) using the Rydberg formula with a reduced mass correction. The energy levels provided are Kα (2,1), Kβ (3,1), Lα (3,2), and Lβ (4,2). The correct calculation for Lβ was performed using the formula 1/λ=RZ²((1/n₁²)-(1/n₂²)), resulting in a wavelength of 0.14 nm for Lβ. However, discrepancies arose in the calculations, prompting questions about the choice of quantum numbers and the atomic number (Z=29).

PREREQUISITES
  • Understanding of the Rydberg formula for hydrogen-like atoms
  • Knowledge of quantum numbers and energy levels in atomic physics
  • Familiarity with the concept of reduced mass in atomic systems
  • Basic skills in performing unit conversions for wavelength calculations
NEXT STEPS
  • Research the Rydberg formula and its application to multi-electron atoms
  • Study the concept of reduced mass and its significance in atomic physics
  • Learn about the energy level transitions in copper and other transition metals
  • Explore common errors in wavelength calculations and how to troubleshoot them
USEFUL FOR

This discussion is beneficial for physics students, particularly those studying atomic physics, as well as educators and professionals involved in X-ray spectroscopy and materials science.

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Homework Statement


Problem: "What are the wavelengths of the characteristic Kα, Kβ , Lα and Lβ x-rays emitted from copper? Remember to use a Rydberg constant with the reduced mass correction made for elemental copper."

Givens:
Energy levels given:

Kα (2,1)

Kβ (3, 1)

Lα (3, 2)

Lβ (4, 2)​

Prompt and energy levels here: https://imgur.com/ygtSCWx

Homework Equations



No relevant equations were provided for this assignment. The prompt hinted to use the Rydberg formula, but since I took into account the mass correction for elemental copper was made. I used the following equation:

1/λ=RZ^2((1/n^2)−(1/n^2))

The Attempt at a Solution


[/B]
For LB (2,1), here is how I calculated the wavelength.

1/λ=RZ^2((1/n^2)−(1/n^2)) = (1.09737*10^7) * ((1/2^2) - (1/4^2))

λ = 0.14 nm

However, WebAssign has marked this wrong. Any suggestions?
 
Last edited:
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Why did you use 2 and 4 for the n values? What value did you use for Z?
 
mjc123 said:
Why did you use 2 and 4 for the n values? What value did you use for Z?
Sorry, meant to say Lβ (4, 2) .For Z, I used 29.
 
How did you get such wildly different numbers for the 4 lines (including one negative)?
 

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