The wavelength of the Kα line for an element of atomic number 57 is λ. What is the wavelength of

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The wavelength of the Kα line for an element of atomic...

The wavelength of the $K_{\alpha}$ line for an element of atomic number 57 is $\lambda$. What is the wavelength of the $K_{\alpha}$ line for the element of atomic number $29 ?$
(a) $\lambda$
(b) $2 \lambda$
(c) $4 \lambda$
(d) $\lambda 4$

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Key Concepts

Moseley’s Law

Moseley’s Law states that the square root of the frequency of characteristic X-ray emissions is proportional to the effective nuclear charge (approximately Z minus a screening constant). This law explains why the X-ray spectral lines of different elements shift systematically with atomic number, making it a crucial tool in understanding atomic structure and validating the concept of atomic numbers as a fundamental property.

K? X-ray Transition

The K? X-ray transition refers to the electronic transition from the L shell (n=2) to the K shell (n=1) in an atom. This transition produces one of the most intense lines in the X-ray spectrum and is highly reproducible across different elements, with its wavelength being inversely related to the square of the effective nuclear charge experienced by the electron.

Effective Nuclear Charge

Effective nuclear charge quantifies the net positive charge experienced by an electron in an atom after accounting for the shielding or screening effects of other electrons. In the context of X-ray emissions, especially for inner-shell electrons, this concept explains how the binding energies and resulting photon wavelengths depend on the number of protons in the nucleus while being moderated by electron-electron interactions.

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