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 × 108 m/s.)
Let `lambda` be the cut off wavelength and V be the operating potential in the X-ray tube.
Then, `lambda = (hc)/V`
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`