An electron, initially at rest is accelerated through a potential difference of 550 V. What is the speed of the electron due to this potential difference?
The speed of the electron due to this potential difference is approximately 2.2 x 10^6 m/s.
To find the speed of the electron due to the potential difference, we can use the formula for the kinetic energy gained by the electron:
K.E. = (1/2)mv^2
Where K.E. is the kinetic energy gained by the electron, m is the mass of the electron, and v is the speed of the electron.
We can also use the formula for the potential energy gained by the electron:
P.E. = qV
Where P.E. is the potential energy gained by the electron, q is the charge of the electron, and V is the potential difference.
Since the electron is accelerated, the potential energy gained is equal to the kinetic energy gained:
K.E. = P.E.
Therefore, we can equate the two formulas:
(1/2)mv^2 = qV
The charge of the electron, q, is equal to the charge of an electron, e, which is approximately 1.6 x 10^-19 coulombs.
With this information, we can solve for the speed, v:
v^2 = (2qV) / m
To find the mass of the electron, m, we can use the known value of the electron rest mass, which is approximately 9.109 x 10^-31 kilograms.
Plugging in the values:
v^2 = (2 x 1.6 x 10^-19 C x 550 V) / 9.109 x 10^-31 kg
Simplifying:
v^2 = 1.76 x 10^-17 C*V / kg
Taking the square root of both sides to solve for v:
v = √(1.76 x 10^-17 C*V / kg)
Calculating this expression will give us the speed of the electron due to the potential difference.
To find the speed of the electron due to the potential difference of 550 V, we can use the equation for the kinetic energy gained by an electron accelerated through a potential difference.
The equation is:
KE = qV
Where:
KE is the kinetic energy gained by the electron,
q is the charge of the electron (1.6 x 10^-19 C),
V is the potential difference (550 V).
The kinetic energy gained by the electron is given by:
KE = (1/2)mv^2
Where:
m is the mass of the electron (9.1 x 10^-31 kg),
v is the speed of the electron.
We can equate the two equations for kinetic energy:
(1/2)mv^2 = qV
Now, let's solve for v:
v^2 = (2qV) / m
v = sqrt((2qV) / m)
Plugging in the values:
v = sqrt((2 * 1.6 x 10^-19 C * 550 V) / 9.1 x 10^-31 kg)
Now, let's calculate the value of v.