an electron is accelerated from rest through a potential difference V. If the electron reaches a speed of 9.11*x10^6 m/s, what is the potential difference?
To determine the potential difference (V), we can use the equation for the kinetic energy of a particle:
K.E. = (1/2)mv^2
Where:
K.E. is the kinetic energy of the electron,
m is the mass of the electron, and
v is the velocity of the electron.
Knowing that the mass of an electron is approximately 9.11 x 10^-31 kg, and the speed of the electron is given as 9.11 x 10^6 m/s, we can calculate the kinetic energy.
K.E. = (1/2) * (9.11 x 10^-31 kg) * (9.11 x 10^6 m/s)^2
Now, the kinetic energy gained by the electron is equal to the potential energy change it experiences when accelerated through a potential difference (V):
K.E. = eV
Where:
e is the elementary charge of an electron (1.6 x 10^-19 C), and
V is the potential difference.
Since we already know the kinetic energy, we can rearrange the equation to solve for V:
V = K.E. / e
Substituting the calculated value of K.E., we can now find the potential difference (V).