Calculate the speed of an electron that is accelerated through the potential difference of 123 V.
To calculate the speed of an electron accelerated through a potential difference, we can use the following formula:
v = sqrt((2*q*V) / m)
where:
v = speed of the electron
q = charge of the electron
V = potential difference
m = mass of the electron
The charge of an electron is approximately -1.6 x 10^-19 C, and the mass of an electron is approximately 9.1 x 10^-31 kg.
Plug in the values into the formula:
v = sqrt((2 * (-1.6 x 10^-19 C) * (123 V)) / (9.1 x 10^-31 kg))
Simplifying the equation further:
v = sqrt((-3.2 x 10^-19 C * V) / (9.1 x 10^-31 kg))
Now, plug in the values to get the final answer:
v ≈ sqrt((-3.2 x 10^-19 C * 123 V) / (9.1 x 10^-31 kg))
Calculating the expression:
v ≈ sqrt((-3.936 x 10^-17 C*V) / (9.1 x 10^-31 kg))
v ≈ sqrt(-4.31538 x 10^13 m^2/s^2)
Since the result is an imaginary number, it means that the electron cannot be accelerated to that speed through a potential difference of 123 V.
To calculate the speed of an electron accelerated through a potential difference, we can use the formula for the kinetic energy of a particle. The kinetic energy (KE) is equal to half the mass (m) times the square of the velocity (v) of the particle:
KE = 1/2mv^2
First, we need to find the kinetic energy of the electron. The electron has a charge of -1.6 x 10^-19 Coulombs (C) and is accelerated through a potential difference of 123 volts (V). The formula to calculate the potential energy (PE) of a charged particle is PE = qV, where q is the charge and V is the potential difference.
PE = qV = (-1.6 x 10^-19 C)(123 V)
Next, we need to equate the potential energy to the kinetic energy. At the start, when the electron is at rest, its kinetic energy is zero. Therefore,
KE = PE
1/2mv^2 = (-1.6 x 10^-19 C)(123 V)
Now, we need to rearrange the formula for v:
v = √(2KE/m)
v = √((2(-1.6 x 10^-19 C)(123 V))/mass of electron)
The mass of an electron is approximately 9.1 x 10^-31 kilograms (kg). Substituting this value and solving the equation will give us the speed of the electron.