Calculate the voltage required to accelerate a beam of protons initially at rest if they have a kinetic energy of 4.5keV.

deltaV = V
Calculate their speed if they have a kinetic energy of 4.5keV .
v = m/s

Same process as the last question.

To calculate the voltage required to accelerate the protons, we can use the equation:

deltaV = V = E / q,

where deltaV is the voltage, E is the kinetic energy, and q is the charge of the proton.

The charge of a proton, q, is equal to the elementary charge, e, which is approximately 1.6 x 10^-19 Coulombs.

Substituting the given values into the equation, we have:

V = 4.5 keV / (1.6 x 10^-19 C).

Now let's convert the kinetic energy from keV to Joules by multiplying it by the conversion factor 1 keV = 1.6 x 10^-16 J:

V = (4.5 x 1.6 x 10^-16 J) / (1.6 x 10^-19 C).

This simplifies to:

V = 4.5 x 10^3 x 10^-16 / 10^-19.

Canceling out units and simplifying further, we have:

V = 4.5 x 10^3 / 10^3.

Finally, calculating the value, we get:

V = 4.5 V.

So, the voltage required to accelerate the protons is 4.5 volts.

To calculate the speed of the protons, we can use the equation:

Kinetic Energy = 0.5 * (mass of proton) * (speed of proton)^2.

Given that the kinetic energy is 4.5 keV, we need to convert it to Joules (as discussed earlier) before using the equation.

Now, rearrange the equation to solve for the speed:

(speed of proton)^2 = (2 * Kinetic Energy) / (mass of proton).

Substituting the values, we have:

(speed of proton)^2 = (2 * 4.5 x 1.6 x 10^-16 J) / (mass of proton).

The mass of a proton is approximately 1.67 x 10^-27 kg.

So,

(speed of proton)^2 = (2 * 4.5 x 1.6 x 10^-16 J) / (1.67 x 10^-27 kg).

Calculating the value:

(speed of proton)^2 = (7.2 x 10^-16 J) / (1.67 x 10^-27 kg).

Canceling out units and simplifying further, we have:

(speed of proton)^2 = 7.2 x 10^11 kg m^2 s^-2.

Taking the square root of both sides, we get:

speed of proton = √(7.2 x 10^11 kg m^2 s^-2).

Finally, calculating the value using a calculator, we get:

speed of proton = 8.49 x 10^5 m/s.

Therefore, the speed of the protons is approximately 8.49 x 10^5 m/s.