If voltage applied to an $$X-ray$$ tube is increased from V $$=$$ $$10$$ kV to $$20$$ kV, the wave length interval between Kα $$-line$$ and cut off wavelength of continuous $$X-ray$$ becomes three times. Take $$Rhce=13.6V$$,$$hc=12420$$ (eV$$−A°$$), where R is Rydberg constant, h is Planck's constant, c is speed of light in vacuum and $$-e$$ is charge on electron.Mark the CORRECT $$statement(s)$$.

Question

If voltage applied to an $$X-ray$$ tube is increased from V $$=$$ $$10$$ kV to $$20$$ kV, the wave length interval between Kα $$-line$$ and cut off wavelength of  continuous $$X-ray$$ becomes three times. Take  $$Rhce=13.6V$$,$$hc=12420$$  (eV$$−A°$$), where R is Rydberg constant, h is Planck's constant, c is speed of light in vacuum and $$-e$$ is charge on electron.Mark the CORRECT $$statement(s)$$.

Infinity Learn · Accepted Answer

Let x be the wave length for Kα $$-line$$λcut $$off=hceVInitially$$ , λcut $$off=hceV1=1242010000A0=1.242A0Finally$$ , λcut $$off=hceV2=1242020000A0=0.621A0Given$$ : x−$$hceV2x$$−$$hceV1=3$$​.................(1)Also$$, $$1$$λ$$=R(Z$$−$$1)2(1$$−$$122)⇒$$x=43R(Z$$−$$1)2$$​.........(2)Solving$$ $$(1) and (2) , we get⇒   $$Z=29$$

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