A 500kV is applied across an X-ray tube. Calculate the maximum velocity of the electrons produced [Me = 9.1 x 10-31kg, e = 1.6 x 10-19C]

Answer Details

The kinetic energy gained by an electron accelerated through a potential difference is given by the equation: KE = eV where KE is the kinetic energy, e is the charge of an electron and V is the potential difference. The maximum velocity of an electron produced by an X-ray tube is given by the equation: v = √(2KE/me) where v is the velocity, KE is the kinetic energy, me is the mass of an electron. Substituting the values given, we have: KE = eV = (1.6 x 10^-19 C) x (500 x 10^3 V) = 8 x 10^-14 J v = √(2KE/me) = √[(2 x 8 x 10^-14 J)/(9.1 x 10^-31 kg)] v = 4.2 x 10^8 m/s Therefore, the maximum velocity of the electrons produced is 4.2 x 10^8 m/s. The answer is (a) 4.2 x 10^8 m/s.