Calc K-Shell X-Ray Series Wavelengths for Zirconium Atom

In summary, the three longest wavelengths for the K-shell x-ray series of the zirconium atom are 79.8832 pm, 67.401142 pm, and 63.90653 pm. The series limit is 56.9543545 pm, calculated using the formula 1/λ = Z^2*R(1/(nl)^2 - 1/(nu)^2) with Z=40, nl=1, and nu=∞. It is possible that there was an error in punching values into the calculator for this calculation.
  • #1
freefallin38
20
0
Calculate the three longest wavelengths and the series limit for the K-shell x-ray series of the zirconium atom.
(a) λ(Kα) = 79.8832 pm
(b) λ(Kβ) = 67.401142 pm
(c) λ(Kγ) = 63.90653 pm
(d) The series limit is _____ pm

So I have solved parts a-c. For part d, the series limit, I tried solving using the following formula:
1/lambda=Z^2*R(1/(nl)^2-1/(nu)^2), where nl=1, nu=infinity, Z=40 so it reduced to:
Lambda=1/(Z^2R)= 56.9543545pm, but this answer is wrong. Can anyone see where I'm going going wrong?
 
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  • #2
At a guess, I'd say you may have punched something into your calculator wrong for part (d). Isn't 3/4 of 79.88 more like 59.91 ?
 

Related to Calc K-Shell X-Ray Series Wavelengths for Zirconium Atom

1. What is the K-Shell X-Ray Series for Zirconium Atom?

The K-Shell X-Ray Series for Zirconium Atom refers to a series of X-ray wavelengths that are emitted when an electron transitions from a higher energy level to the K-shell (the innermost shell) of a Zirconium atom. This series is unique to Zirconium and is used in X-ray spectroscopy to identify and analyze the element.

2. How many wavelengths are in the K-Shell X-Ray Series for Zirconium Atom?

The K-Shell X-Ray Series for Zirconium Atom consists of five wavelengths: Kα1, Kα2, Kβ1, Kβ2, and Kβ3. These wavelengths correspond to different electron transitions within the atom's K-shell and have distinct energies and intensities.

3. What is the significance of the K-Shell X-Ray Series for Zirconium Atom?

The K-Shell X-Ray Series for Zirconium Atom is significant because it provides a unique fingerprint for the element. Each of the five wavelengths in the series is specific to Zirconium and can be used to identify and analyze the element in various materials and compounds.

4. How are the K-Shell X-Ray Series wavelengths for Zirconium Atom calculated?

The K-Shell X-Ray Series wavelengths for Zirconium Atom are calculated using the Rydberg formula, which relates the energy levels of an atom to the wavelength of light emitted during an electron transition. The specific calculations for each wavelength in the series are complex and require knowledge of the atom's electronic structure.

5. Why is it important to know the K-Shell X-Ray Series wavelengths for Zirconium Atom?

Knowing the K-Shell X-Ray Series wavelengths for Zirconium Atom is important for various applications in science and technology. For example, it can be used in X-ray diffraction to determine the crystal structure of zirconium-containing materials. It can also be used in X-ray fluorescence spectroscopy to identify and quantify the amount of zirconium in a sample. Additionally, understanding the K-Shell X-Ray Series can provide valuable insights into the electronic structure and behavior of Zirconium atoms.

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