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If an X-ray tube operates at the voltage...

If an X-ray tube operates at the voltage of 10kV, find the ratio of the de-broglie wavelength of the incident electrons to the shortest wavelength of X-ray producted. The specific charge of electron is `1.8xx10^11 C/(kg)`.

Text Solution

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The correct Answer is:
`0.1`
de - Brogile wavelength when a charge q is accelerated by a potential difference of V volts is
`lambda_(b)=h/(sqrt(2qVm))" ".....(i)`
For cut off wavelength of X - rays , we have `qV = (hc)/(lambda_(m))`
or `lambda_(m) = (hc)/(qV)" "….(ii) `
from eq.(i) and (ii) , we get `(lambda_(b))/(lambda_(m))=((sqrt(qV))/(2m))/c`
For electron `q/m = 1.8 xx 10^(11) `C/kg (given ) . Substituting the values the desired ratio is
`(lambda_(b))/(lambda_(m))=(sqrt((1.8 xx10^(11)xx10xx10^(3))/2))/(3xx10^(8))=0.1 ` .
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