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Atomic numbers of two elements are 31 and 41. Find the ratio of the wavelength of the ${K_alpha }$ are

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4 : 3

9 : 16

16 : 27

16 : 9

answer is D.

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Detailed Solution

$frac{1}{lambda } = R{(z - b)^2}left( {frac{1}{{{n_1}^2}} - frac{1}{{{n_2}^2}}} right)$

$therefore frac{1}{lambda }alpha {(z - b)^2},for,,K - series,b = 1$

$therefore frac{1}{lambda }alpha {(z - 1)^2} Rightarrow,, therefore frac{{{lambda _1}}}{{{lambda _2}}} = {left( {frac{{{z_2} - 1}}{{{z_1} - 1}}} right)^2} = {left( {frac{{41 - 1}}{{31 - 1}}} right)^2} = 16:9$

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