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.

Options

A. 28
B. 29
C. 65
D. 66

Answer

B

Explanation

The cut-off wavelength when `V = V_(1) = 10 kV` is
`lambda_(1) = (h c)/(e V_(1)) = 1243.125 xx 10^(-13) m`
The cut-off wavelength when `V = V_(2) = 20 kV` is
`lambda_(2) = (h c)/(e V_(2)) = 621.56 xx 10^(-13) m`
The wavelength corresponding to `K_(alpha)` line is ,
`(1)/(lambda) = (3R)/(4) (Z - 1)^(2)`
From given information, `(lambda - lambda_(2)) = 3 (lambda - lambda_(1))`
Solving above equation, we get `Z = 29`