An electron at rest of mass 9.11x10^−31 kg is accelerated through a potential difference of 350 V. It then enters some deflecting plates of 50 V with dimensions as shown. Calculate the distance,x, or of the deflection of the electron. The charge on an electron is 1.6x10^−19 C). (20 marks)
Same Question lol
€ = FE /q = 50/0.05 = 1000 N/C
Magnitude of force on electron: 1000 N/C * 1.6x10-19C = 1.6x10-16N
a = F/m = 1.6x10-16N/9.11x10-31 = 1.76x1014 m/s2
1/2mv2
= qv ½*9.11x10-31 *v2
= 350*1.6x10-19 v2
= 2*350*1.6x10-19 /9.11x10-31 v = 1.11x107
m/s time to travel through: t = d/v = 0.25 cm / 1.11x107
m/s = 2.25x10-8s
d = vi*t + ½*a*t2
= 0 + ½*1.76x1014 m/s2
*(2.25x10-8s)2
= 0.044m
The distance x is approximately 0.044m or 4.4 cm.
To calculate the distance of deflection of the electron, we need to consider the electric field created by the potential difference and the dimensions of the deflecting plates.
First, let's determine the kinetic energy gained by the electron when it is accelerated through the potential difference of 350 V.
The potential difference is given by:
V = ΔV = 350 V
The energy gained by the electron can be calculated using the equation:
ΔE = qΔV
where ΔE is the energy gained, q is the charge on the electron, and ΔV is the potential difference.
Plugging in the values:
ΔE = (1.6x10^-19 C) * (350 V)
= 5.6x10^-17 J
Next, let's calculate the speed acquired by the electron using its kinetic energy.
The kinetic energy of an object can be calculated using the equation:
KE = 0.5mv^2
where KE is the kinetic energy, m is the mass, and v is the velocity.
Since the electron is initially at rest, its initial kinetic energy is 0 J. Thus, the gained kinetic energy is equal to its total kinetic energy.
So, we have:
ΔE = 0.5mv^2
Rearranging the equation and plugging in the values:
v^2 = (2ΔE) / m
= (2 * 5.6x10^-17 J) / (9.11x10^-31 kg)
= 1.23x10^13 m^2/s^2
v = √(1.23x10^13 m^2/s^2)
≈ 3.51x10^6 m/s
Now, let's determine the electric field strength within the deflecting plates.
The electric field (E) between the plates is given by the equation:
E = ΔV / d
where E is the electric field, ΔV is the potential difference, and d is the distance between the plates.
Since the potential difference is given as 50 V, we have:
E = (50 V) / d
To find the distance of deflection (x), we need to calculate the force acting on the electron within the electric field. The force (F) acting on a charged particle in an electric field is given by the equation:
F = qE
where F is the force, q is the charge on the electron, and E is the electric field strength.
Plugging in the values:
F = (1.6x10^-19 C) * [(50 V) / d]
= (8x10^-19) / d N
The force acting on the electron can also be calculated using Newton's second law, F = ma, where m is the mass of the electron.
Since the electron is moving perpendicular to the field, the force acting on it is responsible for deflecting it.
So, we can equate the electric force to the centripetal force as follows:
F = m(v^2 / r)
where F is the force, m is the mass, v is the velocity, and r is the radius of curvature.
Since the electron moves in a straight line (without a curved path), the radius of curvature is not applicable in this scenario.
Thus, we have:
F = m(v^2 / r)
= ma
Rearranging the equation, we find:
a = v^2 / r
= v^2 / x
The acceleration of the electron is also given by:
a = F / m
= (8x10^-19) / d / 9.11x10^-31 kg
Setting the two equations for acceleration equal to each other, we get:
v^2 / x = (8x10^-19) / d / 9.11x10^-31 kg
Rearranging the equation and solving for x, we have:
x = (v^2 * d) / [(8x10^-19) / 9.11x10^-31 kg]
= (3.51x10^6 m/s)^2 * d / [(8x10^-19) / 9.11x10^-31 kg]
Plugging in the given values:
x = (3.51x10^6 m/s)^2 * d / [(8x10^-19) / 9.11x10^-31 kg]
After performing the calculations, you will get the final value of x in meters.
To calculate the distance of deflection (x) of the electron, we need to consider the forces acting on the electron.
First, we need to calculate the kinetic energy of the electron after it is accelerated through the potential difference of 350 V. The formula for kinetic energy is given by:
K.E. = (1/2)mv^2
Where:
- K.E. is the kinetic energy,
- m is the mass of the electron, which is 9.11x10^-31 kg,
- v is the final velocity of the electron.
In this case, the electron starts from rest, so its initial velocity (u) is zero. We can use the formula for potential difference to calculate the final velocity (v):
V = qV
Where:
- V is the potential difference,
- q is the charge on the electron,
- V is the final velocity.
Rearranging the formula, we have:
V = qV/m
Now we can substitute the given values:
V = (1.6x10^-19 C)(350 V) / 9.11x10^-31 kg
Simplifying the expression, we can find the final velocity (v) of the electron.
Next, we need to consider the electric field between the deflecting plates. The electric field (E) is given by:
E = V/d
Where:
- E is the electric field,
- V is the potential difference between the plates,
- d is the distance between the plates.
In this case, the potential difference between the plates is 50 V, so we can substitute the values into the formula to find the electric field (E) between the plates.
Once we have the electric field (E), we can calculate the force (F) on the electron:
F = qE
Where:
- F is the force on the electron,
- q is the charge on the electron,
- E is the electric field.
Now, we can use Newton's second law of motion to find the acceleration (a) of the electron:
F = ma
Where:
- F is the force on the electron,
- m is the mass of the electron,
- a is the acceleration.
We substitute the known values and find the acceleration (a).
The electron experiences constant acceleration between the plates. Using the formula of motion:
x = (1/2)at^2
Where:
- x is the distance of deflection,
- a is the acceleration,
- t is the time taken to travel between the plates.
The time (t) can be found using the equation:
s = ut + (1/2)at^2
Where:
- s is the distance between the plates,
- u is the initial velocity (zero),
- a is the acceleration,
- t is the time taken.
Simplifying the equation, we can rearrange it to find t.
Finally, we can substitute the known values into the equation x = (1/2)at^2 to calculate the distance of deflection (x).