Calculate the wavelength of the K_{alpha} lin | vedclass

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(A) Given, $Z=31$ and $a=5 	imes 10^7 \, 	ext{Hz}^{1/2}$.According to Moseley's law for $K_{\alpha}$ lines, $\sqrt{
u} = a(Z-1)$.Squaring both side

Vedclass · Accepted Answer

$1.33 \, \mathring{A}$

Vedclass · Answer

(A) Given, $Z=31$ and $a=5 	imes 10^7 \, 	ext{Hz}^{1/2}$.According to Moseley's law for $K_{\alpha}$ lines, $\sqrt{
u} = a(Z-1)$.Squaring both sides, we get $
u = a^2(Z-1)^2$.Substituting the values: $
u = (5 	imes 10^7)^2 	imes (31-1)^2$.$
u = 25 	imes 10^{14} 	imes 30^2 = 25 	imes 10^{14} 	imes 900 = 2.25 	imes 10^{18} \, 	ext{Hz}$.We know that $\lambda = \frac{c}{
u}$, where $c = 3 	imes 10^8 \, 	ext{m/s}$.$\lambda = \frac{3 	imes 10^8}{2.25 	imes 10^{18}} = 1.33 	imes 10^{-10} \, 	ext{m}$.Since $1 \, \mathring{A} = 10^{-10} \, 	ext{m}$, the wavelength is $1.33 \, \mathring{A}$.

Calculate the wavelength of the $K_{\alpha}$ line for $Z=31$, when $a=5 \times 10^7 \, Hz^{1/2}$ for a characteristic $X$-ray spectrum.

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