A cobalt (atomic$$ no. $$=$$ $$27) target is bombarded with electrons, and the wavelengths of its characteristic $$X-ray$$ spectrum are measured. A second weak characteristic spectrum is also found, due to an impurity in the target. The wavelengths of the Kα lines are $$225.0$$ pm (cobalt) and $$100.0$$ pm (impurity). If the atomic number of the impurity is $$10$$ N. The value of N is $$_________(take$$ b $$=$$ $$1)$$

Question

A cobalt (atomic$$ no. $$=$$ $$27) target is bombarded with electrons, and the wavelengths of its characteristic $$X-ray$$ spectrum are measured. A second weak characteristic spectrum is also found, due to an impurity in the target. The wavelengths of the Kα lines are $$225.0$$ pm (cobalt) and $$100.0$$ pm (impurity). If the atomic number of the impurity is $$10$$ N. The value of N is $$_________(take$$ b $$=$$ $$1)$$

Infinity Learn · Accepted Answer

Using Mosely's law for both cobalt and $$impurityf=K(Z$$−$$b)$$⇒cλ$$=K(Z$$−$$b)$$ $$f=K(Z$$−$$1)$$⇒cλ$$=K(Z$$−$$1)$$∵$$b=1$$⇒ cλ$$co=KZCo$$−$$1$$ and cλ$$x=KZx$$−$$1$$⇒ λcoλ$$x=Zx$$−$$1Zco$$−$$1225100=Zx$$−$$127$$−$$1$$⇒$$ZX=40=4$$×$$10N=4$$

X-rays

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X-rays

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Using Mosely's law for both cobalt and impurityf=K(Z−b)⇒cλ=K(Z−b) f=K(Z−1)⇒cλ=K(Z−1)∵b=1⇒ cλco=KZCo−1 and cλx=KZx−1⇒ λcoλx=Zx−1Zco−1225100=Zx−127−1⇒ZX=40=4×10N=4

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