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

In summary, the wavelength of the characteristic Kα, Kβ, Lα, and Lβ x-rays emitted from copper can be calculated using the Rydberg formula with the reduced mass correction for elemental copper. The values for n and Z used for each line were Kα (2,1), Kβ (3,1), Lα (3,2), and Lβ (4,2), with Z being 29 for copper. However, there seems to be an error in the calculations for the Lβ line, resulting in a negative and incorrect wavelength. It may be necessary to revisit the calculations or seek further clarification.
  • #1
AlphaLibrae
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0

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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  • #2
Why did you use 2 and 4 for the n values? What value did you use for Z?
 
  • #3
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.
 
  • #4
How did you get such wildly different numbers for the 4 lines (including one negative)?
 

1. What is the significance of finding the wavelengths Kα, Kβ, Lα, and Lβ from elemental Cu?

Finding the wavelengths of these specific X-ray emission lines from copper can provide valuable information about the electronic structure of the element, as well as its chemical properties.

2. How are the wavelengths Kα, Kβ, Lα, and Lβ determined for elemental Cu?

The wavelengths are determined through a process called X-ray spectroscopy, where a sample of copper is bombarded with high-energy electrons. The resulting X-ray emissions are then analyzed and the wavelengths are calculated based on their energy levels.

3. Why is copper often used in X-ray spectroscopy to find these specific wavelengths?

Copper is a common element and has well-defined energy levels that correspond to these specific X-ray emission lines. This makes it a convenient and reliable element to use in this type of analysis.

4. Can the wavelengths Kα, Kβ, Lα, and Lβ be used to identify other elements besides Cu?

Yes, the wavelengths of these X-ray emission lines are unique to each element and can be used to identify other elements in a sample. However, the specific energy levels and wavelengths may vary slightly for different elements.

5. How can knowing the wavelengths Kα, Kβ, Lα, and Lβ from elemental Cu be applied in scientific research?

Knowing these wavelengths can aid in the characterization and identification of different materials, as well as in the study of the electronic structure and chemical properties of elements. This information can also be used in various analytical techniques, such as X-ray fluorescence spectroscopy.

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