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  4. If frequency of Kα X-ray emitted from the element with atomic number 31 is v, then the frequency of Kα X-ray emitted from the element with atomic number 51 would be

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Q. If frequency of $K_{\alpha}$ X-ray emitted from the element with atomic number 31 is v, then the frequency of $K_{\alpha}$ X-ray emitted from the element with atomic number 51 would be

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Solution:

According to Moseley's law $\nu \, \propto \, (Z - b)^2$ For $K_{\alpha} $ X-ray , $b = 1 \, \therefore \, \nu \, \propto (Z - 1)^2$ For Z = 31, $\nu \, \propto (31 - 1)^2 \propto (30)^2$ For Z = 51 we get, $\nu_1 \propto (51 - 1)^2 \propto (50)^2$ $\therefore $ $\frac{\nu_1}{\nu} = \left( \frac{50}{30} \right)^2 = \frac{25}{9}$ $\therefore $ $\nu_1 = \frac{25}{9} \nu$