An electron reaches a speed of 3.0 × 107 m/s when released beside the negative plate within a parallel plate accelerator with a gap of 15.0 cm. If the mass of an electron is 9.11 × 10−31 kg, what is the potential difference between the plates?
To find the potential difference between the plates, we can use the equation for the kinetic energy of an object:
KE = (1/2) * m * v^2
Where:
- KE is the kinetic energy
- m is the mass of the electron
- v is the speed of the electron
Since the kinetic energy is equal to the electrical potential energy gained by the electron between the plates, we can equate the two:
KE = electrical potential energy = q * ΔV
Where:
- q is the charge of the electron
- ΔV is the potential difference between the plates
The charge of an electron is given as -1.6 × 10^-19 Coulombs. Rearranging the equation, we have:
ΔV = KE / q
Substituting the values we know:
ΔV = (1/2) * m * v^2 / q
Now we can calculate the potential difference:
ΔV = (1/2) * (9.11 × 10^-31 kg) * (3.0 × 10^7 m/s)^2 / (-1.6 × 10^-19 C)
Simplifying the equation, we get:
ΔV = (1/2) * (9.11 × 10^-31 kg) * (9.0 × 10^14 m^2/s^2) / (-1.6 × 10^-19 C)
ΔV = -0.254 volts
Therefore, the potential difference between the plates is approximately -0.254 volts.