Question

#1

Medical X-Rays are produced by accelerating electrons through a potential difference of 25000 V toward a metallic target. Calculate the relativistic velocity of such X-ray producing electrons.

Answer 1

According to the special relativity,relativistic kinetic energy of an electron accelerated by V volts is given by

( - 1 ) mc² = eV

where m - mass of the electron= 9.1 x 10^-31kg

c - velocity of light = 3 x 10⁸m/s

e - charge of the electron = 1.6 x 10^-19 C

V - potential difference = 25000 V

= (1- v²/c²)^-1/2; v - velocity of the electron

substituting we get

( - 1) x9.1 x 10^-31x( 3x10⁸)² = 1.6 x 10^-19 x25000

( - 1) x 8.19 x 10^-14 = 4 x 10^-15

( - 1) = 4 x 10^-15 / 8.19 x 10^-14 = 0.049

= 1 + 0.049 = 1.049

(1- v²/c²)^-1/2 = 1.049

(1- v²/c²)^-1= (1.049)² = 1.1

(1- v²/c²) = 1/1.1 = 0.91

v²/c² = 1 - 0.91 = 0.09

v²= c² x 0.09

v = 0.3 c = 0.3 x 3 x 10⁸ = 9 x 10⁷ m/s