Answer:
1.187 x 10^8 m/s
Explanation:
the potential of the electric field V = 40 kV = 40000 V
the charge on an electron e = 1.6 x 10^-19 C
The energy of an accelerated electron in an electric field is given as
E = eV
E = 1.6 x 10^-19 x 40000 = 6.4 x 10^-15 J
This energy is equal to the kinetic energy with which the electron moves, according to the conservation of energy.
The kinetic energy = [tex]\frac{1}{2}mv^{2}[/tex]
where
m is the mass of the electron = 9.109 x 10^-31
v is the speed of the electron.
Equating the energy, we have
6.4 x 10^-15 = [tex]\frac{1}{2}*9.109*10^-31*v^{2}[/tex]
6.4 x 10^-15 = 4.55 x 10^-31 [tex]v^{2}[/tex]
[tex]v^{2}[/tex] = 1.41 x 10^16
[tex]x^{2} v = \sqrt{1.41*10^{16}}[/tex] = 1.187 x 10^8 m/s
