The anode (positive terminal) of an X-ray tube is at a potential of +115 000 V with respect to the cathode (negative terminal).

(a) How much work (in joules) is done by the electric force when an electron is accelerated from the cathode to the anode?

(b) If the electron is initially at rest, what kinetic energy does the electron have when it arrives at the anode?

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(a) multiply the voltage by the electron charge in Coulombs. The answer will be in Joules.

(b) same answer. All work done due to the potential energy change is converted to KE

(a) To find the work done by the electric force, we can use the formula:

Work = q * ΔV

Where:
q = charge of the electron (1.6 x 10^-19 C)
ΔV = potential difference between the anode and cathode (115,000 V)

Substituting the values into the formula:

Work = (1.6 x 10^-19 C) * (115,000 V)

Calculating:

Work = 1.84 x 10^-14 J

Therefore, the work done by the electric force is approximately 1.84 x 10^-14 Joules.

(b) The kinetic energy of an object can be calculated using the formula:

Kinetic Energy = (1/2) * m * v^2

Where:
m = mass of the electron (9.11 x 10^-31 kg)
v = velocity of the electron

Since the electron is initially at rest, its initial velocity is 0 m/s. Therefore:

Kinetic Energy = (1/2) * (9.11 x 10^-31 kg) * (0 m/s)^2

Simplifying:

Kinetic Energy = 0 Joules

Hence, the electron has zero kinetic energy when it arrives at the anode.

To calculate the work done by the electric force and the kinetic energy of the electron accelerated from the cathode to the anode, we can use the equations for electric potential energy and kinetic energy.

(a) The work done by the electric force is equal to the change in electric potential energy. The formula for electric potential energy is given by:

Electric Potential Energy = q * V

where q is the charge (in this case the charge of the electron) and V is the electric potential difference (voltage). In this case, the charge of the electron is e = 1.6 x 10^-19 C. The electric potential difference between the anode and cathode is 115,000 V. Hence, we can calculate the work done as follows:

Work Done = e * V

Substituting the values:
Work Done = (1.6 x 10^-19 C) * (115,000 V)

Calculate the result to find the work done.

(b) To find the kinetic energy of the electron when it arrives at the anode, we can use the formula for kinetic energy:

Kinetic Energy = 1/2 * m * v^2

where m is the mass of the electron and v is its velocity. The mass of an electron is approximately 9.11 x 10^-31 kg. We can find the velocity using the equation for kinetic energy and rearrange it as follows:

v = √((2 * Kinetic Energy) / m)

Knowing that the kinetic energy equals the work done by the electric force, we can use the previously calculated work done value to calculate the velocity of the electron. Finally, we can use the velocity to calculate the kinetic energy.

Note that in order to make more precise calculations, we would need to take into account relativistic effects. However, for the purpose of this explanation, we will assume non-relativistic velocities.

Using the above formulas, you can calculate the work done (a) and the kinetic energy of the electron (b).