An electron with a mass of 9.11 *10^31 Kg is accelerated from rest across a set if parallel plates that have a potential difference of 150 v and are separated by 0.80 cm
A) determine the kinetic energy of the electron after it crosses between the plates. (Ans 2.4 * 10-17 )
B) determine the final speed of he electron ( ans 7.3 * 10^6 m/s)
C) determine the acceleration of the electron while it is between the plates. ( ans 3.3 * 10^15 m/s)
D) determine the time required for the electron
to travel across the plates. (Ans 2.2 * 10-9 s)
A.
KE=eU=1.6•10⁻¹⁹•150 =2.4•10⁻¹⁷ J
B.
KE=mv²/2
v=sqrt(2•KE/m)
C.
a= v²/2d
D.
v=at
t=v/a
To calculate the values, we will use the equations related to voltage, kinetic energy, speed, acceleration, and time. Let's go step-by-step:
A) To determine the kinetic energy of the electron after it crosses between the plates, we can use the equation:
Kinetic energy = q * V
where q is the charge of the electron (1.6 * 10^-19 C) and V is the potential difference (150 V).
Substituting the values, we get:
Kinetic energy = (1.6 * 10^-19 C) * (150 V)
= 2.4 * 10^-17 J
Therefore, the kinetic energy of the electron after it crosses between the plates is 2.4 * 10^-17 J.
B) To determine the final speed of the electron, we can use the equation:
Kinetic energy = (1/2) * m * v^2
where m is the mass of the electron (9.11 * 10^-31 kg) and v is the final velocity we want to find.
Rearranging the equation to solve for v:
v = sqrt((2 * kinetic energy) / m)
Substituting the values, we get:
v = sqrt((2 * 2.4 * 10^-17 J) / (9.11 * 10^-31 kg))
= 7.3 * 10^6 m/s
Therefore, the final speed of the electron is 7.3 * 10^6 m/s.
C) To determine the acceleration of the electron while it is between the plates, we can use the equation:
Voltage = electric field * distance
where the electric field is the acceleration (a) and the distance is the separation between the plates (0.80 cm = 0.80 * 10^-2 m).
Rearranging the equation to solve for a:
a = voltage / distance
Substituting the values, we get:
a = (150 V) / (0.80 * 10^-2 m)
= 3.3 * 10^15 m/s^2
Therefore, the acceleration of the electron while it is between the plates is 3.3 * 10^15 m/s^2.
D) To determine the time required for the electron to travel across the plates, we can use the equation:
Distance = (1/2) * a * t^2
where the distance is the separation between the plates (0.80 cm = 0.80 * 10^-2 m), the acceleration is given by the electric field (3.3 * 10^15 m/s^2), and we want to find the time (t).
Rearranging the equation to solve for t:
t = sqrt((2 * distance) / a)
Substituting the values, we get:
t = sqrt((2 * 0.80 * 10^-2 m) / (3.3 * 10^15 m/s^2))
= 2.2 * 10^-9 s
Therefore, the time required for the electron to travel across the plates is 2.2 * 10^-9 s.
To solve this problem, we can use the concept of electric potential energy and the equation relating kinetic energy, electric potential energy, and velocity. Here are the steps to solve each part of the problem:
A) Determine the kinetic energy of the electron after it crosses between the plates:
1. Start by calculating the electric potential energy gained by the electron. The formula for electric potential energy is given by U = qV, where U is the electric potential energy, q is the charge, and V is the potential difference.
- Here, the charge of an electron (e) is approximately 1.6 * 10^(-19) C, and the potential difference (V) is 150 V.
- So, U = (1.6 * 10^(-19) C) * (150 V).
2. The kinetic energy (KE) of the electron is equal to the gain in electric potential energy.
- KE = U.
Therefore, the kinetic energy of the electron after it crosses between the plates is 1.6 * 10^(-19) C * 150 V.
B) Determine the final speed of the electron:
1. Use the formula for kinetic energy: KE = (1/2)mv^2, where KE is the kinetic energy, m is the mass, and v is the velocity.
- Rearrange the equation to solve for velocity: v = sqrt((2 * KE) / m).
2. Plug in the values: KE (found in part A) and mass (given as 9.11 * 10^(-31) kg).
- Calculate: v = sqrt((2 * 1.6 * 10^(-19) C * 150 V) / (9.11 * 10^(-31) kg).
Therefore, the final speed of the electron after it crosses between the plates is sqrt((2 * 1.6 * 10^(-19) C * 150 V) / (9.11 * 10^(-31) kg).
C) Determine the acceleration of the electron while it is between the plates:
1. Use the equation for acceleration: a = (v - u) / t, where a is the acceleration, v is the final velocity, u is the initial velocity (0 m/s since the electron starts from rest), and t is the time taken.
- Rearrange the equation to solve for acceleration: a = v / t.
2. Since the electron is accelerated by the electric field, the acceleration a is equal to the electric field strength E divided by the charge of the electron: a = E / (q/m), where E is the electric field strength.
3. Plug in the values: E = V / d (V is the potential difference, and d is the separation distance between the plates), q/m is the charge-to-mass ratio of an electron (1.76 * 10^(11) C/kg).
- Calculate: a = (V / d) / (1.76 * 10^(11) C/kg).
Therefore, the acceleration of the electron while it is between the plates is (V / d) / (1.76 * 10^(11) C/kg).
D) Determine the time required for the electron to travel across the plates:
1. Use the equation of motion: d = ut + (1/2)at^2, where d is the distance (0.80 cm), u is the initial velocity (0 m/s), a is the acceleration (found in part C), and t is the time taken.
- Rearrange the equation to solve for time: t = sqrt(2d / a).
2. Plug in the values: d = 0.80 cm = 0.008 m, and a (found in part C).
- Calculate: t = sqrt(2 * 0.008 m / (V / d) / (1.76 * 10^(11) C/kg)).
Therefore, the time required for the electron to travel across the plates is sqrt(2 * 0.008 m / (V / d) / (1.76 * 10^(11) C/kg).