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The wavelength of characteristics X-ray  \kappa _{\alpha } line emitted by hydrogen like element is 0.32A0. The wavelength of  \kappa _{\beta } line emitted by the same element is:

 

Option: 1

0.21A^{\circ}


Option: 2

0.27A^{\circ}


Option: 3

0.36A^{\circ}


Option: 4

0.41A^{\circ}


Answers (1)

best_answer

As we learn

Characteristics x-ray -

\nu (frequency)

= Rz^{2}\left ( \frac{1}{n{_{1}}^{2}}-\frac{1}{n{_{2}}^{2}} \right )

- wherein

Characteristics x ray can be defined by knocking out of electron from inner orbit of an atom

 

  \kappa _{\alpha }:        \frac{1}{\lambda _{\alpha }}=    Rz^{2}\left ( \frac{1}{1^{2}}-\frac{1}{2^{2}} \right )=Rz^{2}\left ( \frac{3}{4} \right )

\kappa _{\beta }:            \frac{1}{\lambda _{\beta }}=Rz^{2}\left ( \frac{1}{1^{2}}-\frac{1}{3^{2}} \right )=Rz^{2}\left ( \frac{8}{9} \right )

\frac{\lambda _{\beta }}{\lambda _{\alpha }}=\frac{27}{32}

\lambda _{\beta }=0.27A^{\circ}

 

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