When the voltage applied to an X-ray tube is increased from `V_(1)=10 ` kV to `V_(2)=20` kV, the wavelength difference between limit of the continous X-ray spectrum increases by a factor 3 The atomic number of the element of which the tube anticathode is made will be (30-x), Find Value of x.

Answer

30

Explanation

`lambda_(C_2) = (h)/(eV) = (12375)/(10 xx 10^(3)) Å = 1.2375 Å` (i)
`lambda_(C_1) = 0.61875 Å` (ii)
`(1)/(lambda_(k_alpha)) = (Z - 1)^(2) {(1)/(1) - (1)/(4)} xx 10^(7)` (iii)
It is give
`3 xx (lambda_(k_alpha) - 1.2375) = lambda_(k_alpha) - 0.61875`
`implies lambda_(k_alpha) = 1.54338 Å` (iv)
Putting this value in (iii).
`Z - 1 = 29`
`implies Z = 30`