The intensity of X-rays form a Coolidge tube is plotted against wavelength `lambda` as shown in the figure. The minimum wavelength found is `lambda_c` and the wavelength of the `K_(alpha)` line is `lambda_k`. As the accelerating voltage is increased
(a) `lambda_k - lambda_c` increases (b) `lambda_k - lambda_c` decreases
(c ) `lambda_k` increases (d) `lambda_k` decreases

Options

A. `lambda_(K) - lambda_(C)` increases
B. `lambda_(K) - lambda_(C)`decreases
C. `lambda_(K)` increases
D. `lambda_(K)` increases

Answer

A

Explanation

In case of coolidge tube.
`lambda_(min) = (hc)/(eV) = lambda_(c )` (as given here)
Thus, the cut -off wavelength is inversely proportional to acclerating voltage. As `V` increases `lambda_(c )` decreases.
`lambda_(k)` is the wavelength of `K_(oo)` luine which is a characteristic of an atom and does not depond on accelerating voltage of bombarding electron since `lambda_(k)` always refers to a photon wavelength of transition of `e` from the target element from `2 to 1`
the above two facts lead to the conclusion that `lambda_(k)- lambda_( c)` increases as accelerating voltage is increased.