Q.

An X-ray tube is working at potential of 20 kV. The potential difference is decreased to 10 kV. It is found that the difference of the wavelength of Kα X-ray and the most energetic continuous X-ray becomes 4 times the difference before the change of voltage. The atomic number of the target element is _______________ Take b=1 and 13.4=0.54

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answer is 55.

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Detailed Solution

We use λmin=hc20000e,λmin′=hC10000e Given that 4λα−λmin=λα−λmin′⇒ 3λα=4λmin−λmin′⇒  λα=hC30000e⇒hCλα=30000eBy using the formula of energy of electrons according to Bohr's model and considering shielding effect30000=(13.6)112−122(Z−1)2⇒ Z−1=100517=10034=54Z=54+1=55
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