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Question: The characteristics X- ray wavelength for the lines of the \(k_{\alpha}\)series in elements X and Y ...

The characteristics X- ray wavelength for the lines of the kαk_{\alpha}series in elements X and Y are 9.87Å and 2.29Å respectively. If Moseley’s equationν=4.9×107(Z−0.75)\sqrt{\nu} = 4.9 \times 10^{7}(Z - 0.75) is followed, the atomic numbers of X and Y are

A

12, 24

B

10, 12

C

6, 12

D

8, 10

Answer

12, 24

Explanation

Solution

ν=cλ\nu = \frac{c}{\lambda}

νx=3×1089.87×10−10=5.5132×108\sqrt{\nu_{x}} = \sqrt{\frac{3 \times 10^{8}}{9.87 \times 10^{- 10}}} = 5.5132 \times 10^{8}

νy=3×1082.29×10−10=11.4457×108\sqrt{\nu_{y}} = \sqrt{\frac{3 \times 10^{8}}{2.29 \times 10^{- 10}}} = 11.4457 \times 10^{8}

using Moseley’s equation we get

∴5.5132×108=4.9×107(Zx−0.75)\therefore 5.5132 \times 10^{8} = 4.9 \times 10^{7}(Z_{x} - 0.75) …..(i)

and 11.4457×108=4.90×107(Zy−0.75)11.4457 \times 10^{8} = 4.90 \times 10^{7}(Z_{y} - 0.75) ….. (ii)

On solving equation (i) and (ii) Zx=12,Zy=24.Z_{x} = 12,Z_{y} = 24.