Modern Physics Ques 172
- 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)
Show Answer
Answer:
Correct Answer: 172.$(0.27 $ $\AA)$
Solution:
Formula:
Wavelength Corresponding To Spectral Lines:
- $K _{\alpha}$ corresponds to $n=2$ to $n=1$ and
$K _{\beta}$ corresponds to $n=3$ to $n=1$
Since, $E _{31}>E _{21}$
$\therefore \quad \lambda _{K _{\beta}}<\lambda _{K _{\alpha}} \text { or } \quad \lambda _{K _{\beta}} $ $=\lambda _{K _{\alpha}} \left[\frac{\frac{1}{1^{2}}-\frac{1}{2^{2}}}{\frac{1}{1^{2}}-\frac{1}{3^{2}}}\right] $
$= \quad 0.32 (\frac{3 / 4}{8 / 9})=0.27 \AA$
BETA
