Moseley's law

The Moseley's law (after its discoverer Henry Moseley ) in 1914 describes the energy of - line in the X-ray spectrum , the radiation at the junction of L-shells - electron is emitted to the K shell. Moseley's law is an extension of the Rydberg formula . ${\displaystyle K_{\alpha }}$

In a more general form, this law can also be used to determine the wavelengths of the other lines of the characteristic X-ray spectrum . These wavelengths, like the frequency belonging to the wavelength , are dependent on the ordinal number of the respective chemical element . ${\displaystyle \lambda }$ ${\displaystyle \lambda }$ ${\displaystyle f}$ ${\displaystyle Z}$

${\displaystyle f={\frac {c}{\lambda }}=f_{\mathrm {R} }\,Z_{\text{eff}}^{2}\,\left({\frac {1}{n_{1}^{2}}}-{\frac {1}{n_{2}^{2}}}\right).}$

Where:

• ${\displaystyle c}$- the speed of light
• ${\displaystyle f_{\mathrm {R} }=R\,{\frac {1}{1+{\frac {m_{e}}{M}}}}}$ - adjusted Rydberg frequency
  • ${\displaystyle R=cR_{\infty }}$ - Rydberg frequency
  • ${\displaystyle R_{\infty }}$- the Rydberg constant
  • ${\displaystyle m_{e}}$- the mass of an electron
  • ${\displaystyle M}$- the core mass of the element involved
• ${\displaystyle Z_{\text{eff}}=Z-S}$- the effective atomic number of the element. This is where the difference to the Rydberg formula lies
  • ${\displaystyle Z}$- the atomic number of the element
  • ${\displaystyle S}$- a constant that describes the shielding of the nuclear charge by electrons located between the nucleus and the electron in question.
• ${\displaystyle n_{1}}$, - Principal quantum numbers of the two states (n ₁ = inner, n ₂ = outer shell ). ${\displaystyle n_{2}}$

For the transition of an electron from the second shell (L-shell) to the first shell (K-shell), the so-called -transition, applies , and the corresponding wave number is then Moseley's law for the -line: ${\displaystyle K_{\alpha }}$ ${\displaystyle S\approx 1}$ ${\displaystyle {\tilde {\nu }}}$ ${\displaystyle K_{\alpha }}$

${\displaystyle {\begin{aligned}f_{K_{\alpha }}=c\,{\tilde {\nu }}&=f_{\mathrm {R} }\,(Z-1)^{2}\,\left({\frac {1}{1^{2}}}-{\frac {1}{2^{2}}}\right)\\&=f_{\mathrm {R} }\,(Z-1)^{2}\,\left({\frac {3}{4}}\right).\end{aligned}}}$

Starting shell		Target shell			crossing	Shielding constant
${\displaystyle n_{2}}$	...-Bowl	${\displaystyle n_{1}}$	...-Bowl	${\displaystyle n_{2}-n_{1}}$		${\displaystyle S\approx }$
2	L.	1	K	1	${\displaystyle K_{\alpha }}$	1.0
3	M.	2	L.	1	${\displaystyle L_{\alpha }}$	7.4
3	M.	1	K	2	${\displaystyle K_{\beta }}$	1.8

Individual evidence

1. ^ Henry Moseley: The High-Frequency Spectra of the Elements. Part II. In: Phil. Mag. (=  6 ). tape 27 . Taylor & Francis, London 1914, pp. 703–713 (English, archive.org [accessed February 10, 2020]).