Find the wavelength of K_alpha X-rays. | vedclass

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(A) According to Moseley's law for $K_\alpha$ $X$-rays,the transition occurs from $n_2 = 2$ to $n_1 = 1$.Using the Rydberg formula: $\frac{1}{\lambda_

Vedclass · Accepted Answer

$\frac{1216}{(Z - 1)^2} \ \mathring{A}$

Vedclass · Answer

(A) According to Moseley's law for $K_\alpha$ $X$-rays,the transition occurs from $n_2 = 2$ to $n_1 = 1$.Using the Rydberg formula: $\frac{1}{\lambda_{K\alpha}} = R(Z - 1)^2 \left[ \frac{1}{n_1^2} - \frac{1}{n_2^2} ight]$.Substituting the values: $\frac{1}{\lambda_{K\alpha}} = R(Z - 1)^2 \left[ \frac{1}{1^2} - \frac{1}{2^2} ight] = R(Z - 1)^2 \left[ 1 - \frac{1}{4} ight] = \frac{3R(Z - 1)^2}{4}$.Thus,$\lambda_{K\alpha} = \frac{4}{3R(Z - 1)^2}$.Given that $\frac{1}{R} \approx 912 \ \mathring{A}$,we substitute this into the equation:$\lambda_{K\alpha} = \frac{4}{3} 	imes \frac{912}{(Z - 1)^2} = \frac{1216}{(Z - 1)^2} \ \mathring{A}$.

Find the wavelength of $K_\alpha$ $X$-rays.

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