An electron in an x-ray machine is accelerated through a potential difference of 1x10^4 V before it hits the target. What is the kinetic energy of the electron in electron volts?

To find the kinetic energy of an electron in electron volts (eV), we can use the formula:

Kinetic Energy (in eV) = Charge of Electron × Potential Difference

The charge of an electron is constant and is equal to 1.6x10^(-19) Coulombs. The potential difference given is 1x10^4 V.

So, we can calculate the kinetic energy in eV as follows:

Kinetic Energy = (1.6x10^(-19) C) × (1x10^4 V)

Calculating this expression:

Kinetic Energy = 1.6 × 1 × 10^(-19) × 10^4

To simplify the expression, we can combine the powers of 10:

Kinetic Energy = 1.6 × 10^(-15) eV

Therefore, the kinetic energy of the electron is 1.6 × 10^(-15) eV.

To find the kinetic energy of the electron, we can use the equation:

Kinetic energy (KE) = q*V

Where q is the charge of the electron and V is the potential difference.

The charge of an electron (q) is approximately 1.6x10^-19 coulombs.

Given that the potential difference (V) is 1x10^4 V, we can substitute the values into the equation:

KE = (1.6x10^-19 C) * (1x10^4 V)

Multiplying these values, we get:

KE = 1.6x10^-15 J

Now, we convert joules to electron volts. 1 electron volt (eV) is equal to 1.6x10^-19 J.

To convert the energy to electron volts, we divide the energy in joules by the value of 1 eV:

KE (in eV) = (1.6x10^-15 J) / (1.6x10^-19 J/eV)

Simplifying this expression, we get:

KE (in eV) = 1x10^4 eV

Therefore, the kinetic energy of the electron is 1x10^4 eV.

KE=W=eU=1• 10⁴ eV