Question 617: Atoms & Nuclei

Question

The wavelength of $$k_\alpha$$-line characteristic $$X$$-rays emitted by an element is $$0.32 \mathop A\limits^o$$. The wavelength of the $$k_\beta$$-line emitted by the same element will be

Accepted Answer

$$\begin{aligned}
& \frac{1}{\lambda_\alpha}=R(Z-\alpha)^2\left(\frac{1}{1^2}-\frac{1}{2^2}ight)=\frac{3 R}{4}(Z-\alpha)^2 \
& \frac{1}{\lambda_\beta}=R(Z-\alpha)^2\left(\frac{1}{1^2}-\frac{1}{3^2}ight)=\frac{8}{9} R(Z-\alpha)^2 \
& \frac{\lambda_\beta}{\lambda_\alpha}=\frac{8}{9} 	imes \frac{4}{3}=\frac{32}{37}, \lambda_\beta=0.27 \mathop A\limits^o
\end{aligned}$$

Answer

0.32 $$\mathop A\limits^o$$

Answer

0.39 $$\mathop A\limits^o $$

Answer

0.49 $$\mathop A\limits^o $$

Answer

0.27 $$\mathop A\limits^o$$

Atoms & Nuclei

The wavelength of $k_\alpha-line characteristic X-rays emitted by an element is 0.32 \mathop A\limits^o. The wavelength of the k_\beta$-line emitted by the same element will be

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