An electron is accelerated from rest between two parallel plates that are seperated by 2.20 cm. The potential difference between the two plates is 2.10×103 V. If the electron travels from the negative plate to the positive plate, what will be the speed of the electron as it exits through a small hole in the positive plate? 2.72×107 m/s 2.20×107 m/s 3.24×107 m/s 4.03×106 m/s
Question
An electron is accelerated from rest between two parallel plates that are seperated by 2.20 cm. The potential difference between the two plates is 2.10×103 V. If the electron travels from the negative plate to the positive plate, what will be the speed of the electron as it exits through a small hole in the positive plate? 2.72×107 m/s 2.20×107 m/s 3.24×107 m/s 4.03×106 m/s
Solution
To solve this problem, we can use the principle of conservation of energy. The electron starts with an initial kinetic energy of 0 (since it's at rest) and gains kinetic energy as it is accelerated by the electric field between the plates.
The change in the electron's kinetic energy is equal to the work done on it by the electric field, which is equal to the charge of the electron times the potential difference between the plates.
So, we have:
ΔK.E. = q * V
where: ΔK.E. is the change in kinetic energy, q is the charge of the electron (1.6 * 10^-19 C), and V is the potential difference (2.10 * 10^3 V).
Solving for ΔK.E., we get:
ΔK.E. = (1.6 * 10^-19 C) * (2.10 * 10^3 V) = 3.36 * 10^-16 J
Since the electron starts from rest, this is also its final kinetic energy. The kinetic energy of an object is also given by the equation:
K.E. = 1/2 * m * v^2
where: m is the mass of the electron (9.11 * 10^-31 kg), and v is its speed.
We can set these two expressions for the kinetic energy equal to each other and solve for v:
1/2 * m * v^2 = ΔK.E. v^2 = 2 * ΔK.E. / m v = sqrt(2 * ΔK.E. / m)
Substituting the known values, we get:
v = sqrt(2 * 3.36 * 10^-16 J / 9.11 * 10^-31 kg) = 2.74 * 10^7 m/s
So, the speed of the electron as it exits the positive plate is approximately 2.74 * 10^7 m/s. The closest answer to this is 2.72×10^7 m/s.
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