In X-ray tube , when the accelerating voltage `V` is halved, the difference between the wavelength of `K_(alpha)` line and minimum wavelength of continuous X-ray spectrum

Options

A. remains constant
B. becomes more than two times
C. becomes half
D. becomes less than two times

Answer

D

Explanation

`lambda_("min")` is minimm wavelength of continous X-
`lambda_("min") = (hc)/E`
Energy, E = eV
`lambda_("min") = (hc)/(eV)`........... eq. 1
where, V is the voltage appled
`Deltalambda` =Now, if V is halved, AKq will not be changed as the energy between the two shells remain same and Xmin becomes doubled from eq
Now, `Deltalambd. = lambdaK_(alpha) - lambda_("min")^(.)`
`Deltalambda^(.) = lambdaK_(alpha) - 2lambda_("min")`
From eq 3 putting in above equation.
`Deltalambda^(.) = lambdaK_(alpha) - 2(lambdaK_(alpha) - Deltalambda)`
So, `2Deltalambda gt Deltalambda^(.)`