Question

An evacuated tube uses an accelerating voltage of 55 kV to accelerate electrons to hit a copper plate and produce x rays. Non-relativistically, what would be the maximum speed of these electrons?

Answer 1

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

$\frac{1}{2}mv^2 = eV$

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,

$\frac{1}{2}(9.1\ x\ 10^{-31}\ kg)(v)^2 = (1.6\ x\ 10^{-19}\ C)(55000\ V)\\\\v^2 = \frac{(2)(8.8\ x\ 10^{-16}\ J)}{9.1\ x\ 10^{-31}\ kg}\\\\v = \sqrt{19.34\ x\ 10^{14}\ m^2/s^2}$

v = 4.4 x 10⁷ m/s