#### Question

If the operating potential in an X-ray tube is increased by 1%, by what percentage does the cutoff wavelength decrease?

(Use Planck constant h = 6.63 × 10^{-34} Js= 4.14 × 10^{-15} eVs, speed of light c = 3 × 10^{8} m/s.)

#### Solution

Let `lambda` be the cut off wavelength and V be the operating potential in the X-ray tube.

Then, `lambda = (hc)/V`

Here,

h = Planck's constant

c = Speed of light

If the operating voltage is increased by 1%, then the new operating voltage (V') will be given by

`V^' = V + 1/100 xx V`

`V^' = 1.01 "V"`

Cut off wavelength (`lambda^'`) on increasing the operating voltage is given by

`lambda^' = (hc)/(1.01 "V") = lambda/1.01`

`therefore lambda^' - lambda = 0.01/1.01lambda`

Percentage change in the wavelength is given by

`(0.01lambda)/(1.01 xx lambda) xx 100 = 1/1.01`

= 0.9901

=1 (approx.)