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  • The wave length of the characteristic X-ray line emitted by a hydrogen like atom is <

The wave length of the characteristic X-ray \mathrm{K}_\alpha line emitted by a hydrogen like atom is 0.32 \AA. The wave length of \mathrm{K}_\beta line emitted by the same element is:

Option: 1

0.18 \AA


Option: 2

0.48 \AA


Option: 3

0.27 \mathrm{~A}


Option: 4

0.38 \AA


Answers (1)

best_answer

The wavelength of x -rays emitted for K_\alpha line and  K_\beta line are given by \lambda_a=\frac{h c}{E_K-E_L} and 

\lambda_\beta=\frac{h c}{E_K-E_M}

\therefore \frac{\lambda_\alpha}{\lambda_\beta}=\frac{E_K-E_M}{E_K-E_L}=\frac{\frac{1}{1}-\frac{1}{3^2}}{\frac{1}{1}-\frac{1}{2^2}}=\frac{32}{27}

\therefore \lambda_\beta=\frac{27}{32} \times \lambda_\alpha=\frac{27}{32} \times 0.32=0.27 \AA

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Rishi

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