how much kinetic energy will an electron gain in J and eV if it accelerates through a potential difference of 23,000 volts
23,000 eV. For Joules, multiply by the electron charge, in coulombs.
To calculate the kinetic energy gained by an electron when accelerating through a potential difference, you can use the following formulas:
1. In joules (J):
The formula to calculate the kinetic energy (K) in joules is given by:
K = e * V
where e is the charge of an electron (approximately 1.602 x 10^-19 C) and V is the potential difference.
2. In electronvolts (eV):
The formula to calculate the kinetic energy in electronvolts is given by:
K(eV) = V
Let's calculate the kinetic energy gained by the electron:
1. In joules (J):
K(J) = e * V
= (1.602 x 10^-19 C) * (23,000 V)
≈ 3.686 x 10^-15 J
So, the electron gains approximately 3.686 x 10^-15 joules of kinetic energy.
2. In electronvolts (eV):
K(eV) = V
= 23,000 eV
Therefore, the electron gains 23,000 electronvolts of kinetic energy when it accelerates through a potential difference of 23,000 volts.
To determine the kinetic energy gained by an electron when it accelerates through a potential difference of 23,000 volts, we can utilize the formula for the kinetic energy of a charged particle:
Kinetic Energy (K.E.) = q * V
Where:
K.E. is the kinetic energy
q represents the charge of the electron (1.6 x 10^-19 Coulombs)
V is the potential difference
First, let's calculate the kinetic energy in joules (J):
K.E. = q * V
= (1.6 x 10^-19 C) * (23,000 V)
≈ 3.68 x 10^-15 J
Therefore, the kinetic energy gained by the electron is approximately 3.68 x 10^-15 joules.
Now, let's convert this value to electron volts (eV). The conversion factor is 1 eV = 1.6 x 10^-19 J.
K.E. (eV) = K.E. (J) / (1.6 x 10^-19 J)
= (3.68 x 10^-15 J) / (1.6 x 10^-19 J)
≈ 23 eV
Hence, the kinetic energy gained by the electron when it accelerates through a potential difference of 23,000 volts is approximately 3.68 x 10^-15 joules (J) or 23 electron volts (eV).