if electrons are caused to fall through a potential difference of 100000 volt,determine their final speed if they were initially at rest.
To determine the final speed of electrons falling through a potential difference of 100,000 volts, we need to apply the concept of electric potential energy and kinetic energy.
When an electron falls through a potential difference, its electric potential energy is converted to kinetic energy. The change in electric potential energy (ΔPE) is given by the equation:
ΔPE = qΔV
Where,
ΔPE = Change in electric potential energy
q = Charge of the electron (1.6 x 10^-19 coulombs)
ΔV = Potential difference (100,000 volts)
The change in electric potential energy is equal to the kinetic energy of the electron. So we have:
KE = ΔPE
Now, the kinetic energy (KE) of an object is given by the equation:
KE = (1/2)mv^2
Where,
KE = Kinetic energy
m = Mass of the electron (9.1 x 10^-31 kilograms)
v = Velocity (final speed) of the electron
Equating the expressions for kinetic energy and change in electric potential energy, we get:
(1/2)mv^2 = qΔV
Now, let's plug in the values:
(1/2)(9.1 x 10^-31 kg)(v^2) = (1.6 x 10^-19 C)(100,000 V)
Simplifying the equation, we can calculate the final speed (v):
v^2 = [(1.6 x 10^-19 C)(100,000 V)] / [(1/2)(9.1 x 10^-31 kg)]
v^2 = (1.6 x 10^-19 C x 100,000 V) / (4.55 x 10^-31 kg)
v^2 ≈ 3.516 x 10^20 m^2/s^2
Taking the square root of both sides, we find:
v ≈ 1.87 x 10^10 m/s
Therefore, the final speed (velocity) of the electrons would be approximately 1.87 x 10^10 meters per second.