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

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(A) Given: Atomic number $Z=31$ and constant $a=5 	imes 10^7 	ext{ Hz}^{1/2}$.According to Moseley's Law for the $K_{\alpha}$ line:$\sqrt{
u} = a(Z

Vedclass · Accepted Answer

$1.33 	ext{ Å}$

Vedclass · Answer

(A) Given: Atomic number $Z=31$ and constant $a=5 	imes 10^7 	ext{ Hz}^{1/2}$.According to Moseley's Law for the $K_{\alpha}$ line:$\sqrt{
u} = a(Z-1)$Squaring both sides:$
u = a^2(Z-1)^2$Substitute the values:$
u = (5 	imes 10^7)^2 	imes (31-1)^2$$
u = 25 	imes 10^{14} 	imes 30^2$$
u = 25 	imes 10^{14} 	imes 900 = 2.25 	imes 10^{18} 	ext{ Hz}$Now, using the relation $\lambda = \frac{c}{
u}$ where $c = 3 	imes 10^8 	ext{ m/s}$:$\lambda = \frac{3 	imes 10^8}{2.25 	imes 10^{18}}$$\lambda = 1.33 	imes 10^{-10} 	ext{ m}$Since $1 	ext{ Å} = 10^{-10} 	ext{ m}$, we get:$\lambda = 1.33 	ext{ Å}$.

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

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