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

v = 4.4 x 10⁷ m/s

Step-by-step explanation:

The kinetic energy of the electrons will be equal to the energy supplied by the electric voltage:

Kinetic Energy = Electric Energy

`(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,

`(1)/(2)(9.1\ x\ 10^(-31)\ kg)(v)^2 = (1.6\ x\ 10^(-19)\ C)(55000\ V)\\\\v^2 = ((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