When voltage of an X-ray tube is changed from 10 KV to 20 KV, the difference between K α wave length and cut-off wavelength becomes 3 times. Find atomic number of target element.

Question

When voltage of an X-ray tube is changed from 10 KV to 20 KV, the difference between K α ​ wave length and cut-off wavelength becomes 3 times. Find atomic number of target element.

TestHub · Accepted Answer

λ K α ​ − e V 1 ​ h c ​ λ K α ​ − e V 2 ​ h c ​ ​ = 3 , V 1 ​ = 10 kV , V 2 ​ = 20 kV Let Kα photon energy be E (keV): E 1 ​ − 10 1 ​ E 1 ​ − 20 1 ​ ​ = 3 ⇒ E 1 ​ − 20 1 ​ = E 3 ​ − 10 3 ​ ⇒ E = 8 keV ( Z − 1 ) 2 × 4 3 ​ × 13.6 eV = 8000 eV ⇒ ( Z − 1 ) 2 = 784 ⇒ Z − 1 = 28 Z = 29

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