How much kinetic energy is gained by an electron that is allowed to move freely through a potential
difference of 2.5 × 104 V?
The kinetic energy gained by the electron is equal to the potential difference multiplied by the charge of the electron, which is 1.6 x 10^-19 Coulombs. Therefore, the kinetic energy gained by the electron is 4 x 10^-15 Joules.
To calculate the kinetic energy gained by an electron moving freely through a potential difference, we can use the equation:
Kinetic energy (KE) = q * ΔV,
where q is the charge of the electron and ΔV is the potential difference.
The charge of an electron is approximately -1.6 × 10^-19 Coulombs (C).
Given a potential difference of 2.5 × 10^4 V, we can substitute these values into the equation:
KE = (-1.6 × 10^-19 C) * (2.5 × 10^4 V)
Calculating this expression gives us:
KE = -4.0 × 10^-15 Joules (J).
However, since kinetic energy cannot be negative, we take the absolute value of the result:
|KE| = 4.0 × 10^-15 J.
Therefore, the kinetic energy gained by the electron moving freely through a potential difference of 2.5 × 10^4 V is approximately 4.0 × 10^-15 J.
To determine the kinetic energy gained by an electron moving through a potential difference, you can use the equation:
Kinetic Energy (KE) = q × V
where KE is the kinetic energy, q is the charge of the electron, and V is the potential difference.
The charge of an electron is approximately -1.6 × 10^-19 coulombs (C). The potential difference (V) in this case is given as 2.5 × 10^4 volts (V).
Now let's substitute the values into the equation:
KE = (-1.6 × 10^-19 C) × (2.5 × 10^4 V)
First, let's simplify the numbers:
KE = (-1.6) × (2.5) × (10^-19) × (10^4)
Next, we'll perform the calculations:
KE = -4 × 10^-15 joules (J)
Therefore, the kinetic energy gained by the electron is approximately -4 × 10^-15 J. Note that the negative sign indicates that the electron is likely decelerating or moving against an electric field.