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 $$13.4=0.54$$

Question

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 $$13.4=0.54$$

Infinity Learn · Accepted Answer

We use λ$$min=hc20000e$$,λmin′$$=hC10000e$$ Given that $$4$$λα−λ$$min=$$λα−λmin′⇒ $$3$$λα$$=4$$λmin−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−$$1=100517=10034=54Z=54+1=55$$

X-rays

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material