The speed of the electrons on reaching the screen can be determined using the principle of conservation of energy. The electric potential energy gained by an electron when it moves through an electric field is given by the equation:

ΔPE = q * ΔV

where ΔPE is the change in potential energy, q is the charge of the electron, and ΔV is the change in electric potential.

In this case, the electric field has a constant magnitude of 105 V/m. If we assume the distance between the filament and the screen is d meters, then the change in electric potential is:

ΔV = E * d
ΔV = 105 V/m * d m
ΔV = 105d V

The charge of an electron is approximately -1.6 x 10^-19 C. Therefore, the change in potential energy is:

ΔPE = (-1.6 x 10^-19 C) * (105d V)
ΔPE = -1.68d x 10^-17 J

According to the conservation of energy, the change in potential energy is equal to the change in kinetic energy:

ΔKE = ΔPE

The kinetic energy of an object is given by the equation:

KE = (1/2) * m * v^2

where KE is the kinetic energy, m is the mass of the object, and v is the velocity.

Since the mass of an electron is approximately 9.11 x 10^-31 kg, we can solve for the velocity:

(1/2) * (9.11 x 10^-31 kg) * v^2 = -1.68d x 10^-17 J

Solving for v gives:

v = sqrt((-1.68d x 10^-17 J) / (0.5 * 9.11 x 10^-31 kg))
v = sqrt(3.68d x 10^13 m^2/s^2)

Without knowing the exact distance d, we cannot calculate the exact speed. However, if we assume d = 1 m for simplicity, we get:

v = sqrt(3.68 x 10^13 m^2/s^2)
v = 6.07 x 10^6 m/s

This is closest to option e. 3.7x10^6 ms^-1. So, the correct answer is likely (e) 3.7x10^6 ms^-1.

Question

The speed of the electrons on reaching the screen can be determined using the principle of conservation of energy. The electric potential energy gained by an electron when it moves through an electric field is given by the equation:

ΔPE = q * ΔV

where ΔPE is the change in potential energy, q is the charge of the electron, and ΔV is the change in electric potential.

In this case, the electric field has a constant magnitude of 105 V/m. If we assume the distance between the filament and the screen is d meters, then the change in electric potential is:

ΔV = E * d
ΔV = 105 V/m * d m
ΔV = 105d V

The charge of an electron is approximately -1.6 x 10^-19 C. Therefore, the change in potential energy is:

ΔPE = (-1.6 x 10^-19 C) * (105d V)
ΔPE = -1.68d x 10^-17 J

According to the conservation of energy, the change in potential energy is equal to the change in kinetic energy:

ΔKE = ΔPE

The kinetic energy of an object is given by the equation:

KE = (1/2) * m * v^2

where KE is the kinetic energy, m is the mass of the object, and v is the velocity.

Since the mass of an electron is approximately 9.11 x 10^-31 kg, we can solve for the velocity:

(1/2) * (9.11 x 10^-31 kg) * v^2 = -1.68d x 10^-17 J

Solving for v gives:

v = sqrt((-1.68d x 10^-17 J) / (0.5 * 9.11 x 10^-31 kg))
v = sqrt(3.68d x 10^13 m^2/s^2)

Without knowing the exact distance d, we cannot calculate the exact speed. However, if we assume d = 1 m for simplicity, we get:

v = sqrt(3.68 x 10^13 m^2/s^2)
v = 6.07 x 10^6 m/s

This is closest to option e. 3.7x10^6 ms^-1. So, the correct answer is likely (e) 3.7x10^6 ms^-1.

Knowee AI · Accepted Answer