# An electron with an initial speed of 5.50×105 m/s is brought to rest by an electric field.

General guidance

Concepts and reason

The main concept used to solve the given problem is conservation of Energy.
From the conservation of the energy principle, energy neither be created nor be distorted it can be converted into one form of energy into another form of energy.
Initially, from the definition of the kinetic energy, the energy of the electron is calculated. Finally, from the expression of the kinetic energy, it depends on the mass of the object and the velocity of the object.

Fundamentals

The principle of conservation of energy states that the total energy of the system remains constant. The total energy mainly includes kinetic energy and potential energy.
The expression of the kinetic energy is equal to,

Here, is the kinetic energy,is the mass of the object and is the velocity of the object.

Step-by-step

Step 1 of 4

(a)
Calculate the kinetic energy of the electron.
The expression of the kinetic energy of electron is equal to,

Substituteforand forin the above expression of the kinetic energy.

From the definition, the kinetic energy of the electron is determined. From the definition kinetic energy depends on the mass and velocity of the object.

Use the expression of change in kinetic energy to the calculation of the electron potential.

Step 2 of 4

The expression of the change in kinetic energy is equal to,

Substitute for and for in the above expression of the change in kinetic energy.

From the expression of the energy conservation, the change in kinetic energy is equal to the potential energy.

Substitute for in the above expressions of the energy conservation.

The expression of the potential energy is equal to,

Rearrange the above expression in the form of.

Substitute forand for in the above expression of the voltage equation

Since the charge of an electron is negative, hence is negative. Therefore, the electron goes from higher potential to lower potential.

Part a
The electron enters a region of lower potential.

Front the conservation of the energy principle the change in kinetic energy is equal to the change in the potential energy of the system.

All the unit are in the same dimension. Therefore, first convert all the unit carefully. Do not use the expression to the calculation of the potential difference.

Use the differential equation of the change in energy for the calculation of the potential difference that stopped the electron.

Step 3 of 4

(b)
The expression for the change in kinetic energy forms the conservation of the energy principle is equal to.

Substitute for in the above expressions of the energy conservation.

The expression of the potential energy is equal to

Rearrange the above expression in the form of.

Substitute forand for in the above expression of the voltage equation,

For electron, the potential difference is equal to,

Part b
The potential difference that stopped the electron is.

The total energy of a system is always conserved.

Potential energy and potential are two different concepts. If the question asked what the potential energy of the electron is, then the answer would be higher. But, here the potential is asked and since the particle is an electron, the potential will be the negative of the potential energy.

Use the expression of the kinetic energy to the calculation of the kinetic energy of the electron.

Step 4 of 4

(c)
Calculate the kinetic energy of the electron.
The expression of the kinetic energy of electron is as follows:

Substitute for and forin the above expression of the kinetic energy.

Part c
The initial Kinetic energy of the electron is.

Kinetic energy is proportional to the square of the velocity of the electron.

Do not the expression to the calculation of the electron kinetic energy. The conversion of units must be done carefully. Therefore, use the correct expression of the kinetic energy.

Part a
The electron enters a region of lower potential.

Part b
The potential difference that stopped the electron is.

Part c
The initial Kinetic energy of the electron is.

Part a
The electron enters a region of lower potential.

Part b
The potential difference that stopped the electron is.

Part c
The initial Kinetic energy of the electron is.

KEN-my
лш з’я
9.11×10-9 kg
5.5×10 m/s
KE=(9.11×10″ kg)(5.5*10^ m/s) = 1.376×101″} +(1.376×10* )(1.6.4.0-1) =0.861 eV
AKE = KE-KE
0.861 eV
AKE=0-0.861 eV = -0.861 eV
AU =-AK
-0.861 eV
AU = 0.861 eV
ΔU = ΔΥq
AV =49 40
0.861 eV
1.6×10-C
0.861 eV AV = 1.6×10-19 C (0.861 ev) 1×10-“”) (0.861 e lev 1.6×10-C = 0.861 V
AV =qAU
AU =-AK
-0.861 eV
AU = 0.861 eV
ΔU = ΔΥq
AV =49 40
0.861 eV
1.6×10-C
0.861 eV AVE 1.6×10-“C (0.861 ev) 1.6×10-19 ) 1eV 1.6×10-” C =0.861 V
AV = -0.861 V
KE = – my
9.11×10- kg
5.5×109 m/s
KE = (?)(0.11×10 ” kB)(5.5×109 m/s) =1.37×10-1° ) = (1.37×10″ 1) (1 65300 ) =0.86 eV
KE = -mv
0.861 v
0.861 v
0.489 V.
0.354 V
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