Answer:
v = 4.4 x 10⁷ m/s
Explanation:
The kinetic energy of the electrons will be equal to the energy supplied by the electric voltage:
Kinetic Energy = Electric Energy
[tex]\frac{1}{2}mv^2 = eV[/tex]
where,
m = mass of electron = 9.1 x 10⁻³¹ kg
v = speed of electron = ?
e = charge on electron = 1.6 x 10⁻¹⁹ C
V =Voltage = 55 kV = 55000 V
Therefore,
[tex]\frac{1}{2}(9.1\ x\ 10^{-31}\ kg)(v)^2 = (1.6\ x\ 10^{-19}\ C)(55000\ V)\\\\v^2 = \frac{(2)(8.8\ x\ 10^{-16}\ J)}{9.1\ x\ 10^{-31}\ kg}\\\\v = \sqrt{19.34\ x\ 10^{14}\ m^2/s^2}[/tex]
v = 4.4 x 10⁷ m/s
