$(a)\;82\qquad(b)\;41\qquad(c)\;20\qquad(d)\;10$

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Answer : (b) 41

Explanation :

For $\;K_{\alpha}\;$ X-ray line,

$\large\frac{1}{\lambda_{\alpha}}=R\;(z-1)^2 \;[1-\large\frac{1}{2^2}]$

$=R\;(z-1)^2\;[1-\large\frac{1}{4}]$

$\large\frac{1}{\lambda_{\alpha}}=\large\frac{3}{4}\;R\;(z-1)^2----(1)$

$\lambda_{\alpha}=0.76A^{0}=0.76\times10^{-10}m$

$R=1.097\times10^{7} m$

$(z-1)^2=\large\frac{4}{3}\times\large\frac{1}{0.76\times10^{-10}\times1.09\times10^{7}}$

$\approx 1600$

$z-1=40$

$z=41\;.$

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