if electron are caused to fall through a potential difference of 100000 voltage , determine their final speed if they were initially at rest.
Kinetic Energy = e*V = (1/2)_mv^2
v = sqrt[2eV/m]
V = 100,000 volts (capital V)
e and m are the electron charge and mass in SI units.
Solve for velocity v (lower case)
To determine the final speed of electrons falling through a potential difference of 100000 volts, we can use the concept of electrical potential energy and convert it into kinetic energy.
First, we'll need to know the charge of an electron, which is approximately -1.6 x 10^-19 coulombs (C). The voltage, or potential difference, is measured in volts (V).
The potential energy gained by an electron falling through a potential difference can be calculated using the formula:
Potential Energy (PE) = Charge (Q) × Voltage (V)
Since we know that the electron charge (Q) is -1.6 x 10^-19 C and the voltage (V) is 100000 V, we can substitute these values into the equation:
PE = (-1.6 x 10^-19 C) × (100000 V)
Now, we need to convert the potential energy gained into kinetic energy. The kinetic energy (KE) can be calculated using the formula:
Kinetic Energy (KE) = (1/2) × Mass (m) × Velocity (v)^2
Here, the mass of an electron (m) is approximately 9.11 x 10^-31 kilograms (kg), and the velocity (v) is what we want to find.
We equate the gained potential energy (PE) to the kinetic energy (KE):
PE = KE
(-1.6 x 10^-19 C) × (100000 V) = (1/2) × (9.11 x 10^-31 kg) × (v)^2
Now we can solve for the final speed (v):
(v)^2 = [(-1.6 x 10^-19 C) × (100000 V)] / [(1/2) × (9.11 x 10^-31 kg)]
v = √{ [(-1.6 x 10^-19 C) × (100000 V)] / [(1/2) × (9.11 x 10^-31 kg)] }
After substituting the values into the equation and performing the calculations, we get:
v = 5.93 x 10^6 m/s
Therefore, the final speed of the electron, when initially at rest and falling through a potential difference of 100000 volts, is approximately 5.93 x 10^6 meters per second.