Modern Physics 4 Question 30
31. The wavelength of the characteristic X-ray $K _{\alpha}$ line emitted by a hydrogen like element is $0.32 D$. The wavelength of the $K _{\beta}$ line emitted by the same element will be
(1990, 2M)
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Solution:
- $K _{\alpha}$ corresponds to $n=2$ to $n=1$ and $K _{\beta}$ corresponds to $n=3$ to $n=1$
Since, $E _{31}>E _{21}$
$$ \begin{gathered} \therefore \quad \lambda _{K _{\beta}}<\lambda _{K _{\alpha}} \text { or } \quad \lambda _{K _{\beta}}=\lambda _{K _{\alpha}} \frac{\frac{1}{1^{2}}-\frac{1}{2^{2}}}{\frac{1}{1^{2}}-\frac{1}{3^{2}}} \\ =0.32 \frac{3 / 4}{8 / 9}=0.27 \AA \end{gathered} $$
