the electron beam in a television tube consists of electrons accelerated from rest through a potential difference of about 20000v.what is the speed of the electrons?(ignore relativistic effects).electron rest mass is 9.11 X 10^-31kg and electron charge is 1.6 x 10^-19
Ke = (1/2) m v^2 = 20000 volts * electron charge
ChangePE + changeKE = 0.
the change in potential energy of electron is = dPE = qdV = (-e)dV.
The change in kinetic energy of electron is = 1/2mV^2 - 0 = 1/2mV^2.
put these together and get.
(-e)dV + 1/2mV^2 = 0.
1/2mV^2 = (e)dV.
mV^2 = 2(e)dV.
V^2 = 2edV/m.
Insert the figures
V^2 = 2(1.60 * 10^-19C)(20000V)/(9.11 * 10^-31Kg) = 7.0 * 10^15
V = ¡Ì7.0 * 10^15 = 8.4 * 10^7m/s
To find the speed of the electrons, we need to use the concept of kinetic energy. The kinetic energy (K) of an object is given by the formula:
K = (1/2)mv^2
where m is the mass of the object and v is its speed.
In this case, the electrons are accelerated through a potential difference, which converts electrical potential energy into kinetic energy. The potential difference (V) is given as 20,000 volts.
The potential difference (V) is defined as the change in electrical potential energy (U) per unit charge (Q):
V = U/Q
The electrical potential energy (U) is given by:
U = QV
Since the charge (Q) of an electron is 1.6 x 10^-19 coulombs, we can substitute these values into the equation:
U = (1.6 x 10^-19 C)(20,000 V)
U = 3.2 x 10^-15 J
Now, we can equate this electrical potential energy (U) to kinetic energy (K) and find the speed (v) of the electrons:
K = U
(1/2)mv^2 = 3.2 x 10^-15 J
Simplifying the equation:
mv^2 = 6.4 x 10^-15 kg.m^2/s^2
Dividing both sides by the mass of the electron (m = 9.11 x 10^-31 kg):
v^2 = (6.4 x 10^-15 kg.m^2/s^2) / (9.11 x 10^-31 kg)
v^2 = 7.03 x 10^15 m^2/s^2
Taking the square root of both sides:
v ≈ 2.65 x 10^7 m/s
Therefore, the speed of the electrons is approximately 2.65 x 10^7 m/s when accelerated through a potential difference of 20,000 V.