The wavelength of Kα line of zinc (atomic number 30 ) if Kα line from molybdenum (atomic number

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The wavelength of Kα line of zinc (atomic number 30 ) if Kα...

The wavelength of $K_{\alpha}$ line of zinc (atomic number 30 ) if $K_{\alpha}$ line from molybdenum (atomic number $=42$ ) has a wavelength of $0.7078 \AA$ is :
(a) $4.414 \mathrm{~A}$
(b) $1.4148 \mathrm{~A}$
(c) $2.375 \AA$
(d) $1.792 \mathrm{~A}$

Key Concepts

Atomic Number and Effective Nuclear Charge

The atomic number of an element, which denotes the number of protons in its nucleus, plays a pivotal role in determining the energy levels of electrons. As the atomic number increases, the effective nuclear charge experienced by the electrons also increases, leading to a stronger attraction between the nucleus and the electrons. This change in effective nuclear charge influences the energy differences between electron shells, thereby affecting the wavelengths of emitted X-rays during electron transitions.

Characteristic X-rays and K? Line

Characteristic X-rays are produced when an inner-shell electron is removed and an electron from a higher energy level falls into the vacant lower energy state, emitting radiation. The K? line is the result of an electron transition from the L-shell to the K-shell. It is one of the most prominent lines in X-ray spectroscopy, and its wavelength is sensitive to the atomic number of the element emitting it, making it a valuable tool in element analysis.

Moseley’s Law

Moseley’s Law establishes a relationship between the frequency of the characteristic X-rays emitted by an element and its atomic number. Specifically, it shows that the square root of the frequency of the K-series lines (like the K? line) is proportional to the difference between the atomic number and a screening constant. This law is critical in understanding how variations in atomic number lead to shifts in the X-ray spectra and helps in determining the electronic structure of elements.

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