Electrons in an x-ray machine are accelerated from rest through a potential difference of 60 000 V.What is the kinetic energy of each of these electrons in eV?
A)60 eV
B)96 eV
C)38 eV
D)60 keV
E)120 eV

Question

Electrons in an x-ray machine are accelerated from rest through a potential difference of 60 000 V.What is the kinetic energy of each of these electrons in eV?
A)60 eV
B)96 eV
C)38 eV
D)60 keV
E)​120 eV

Quizplus · Accepted Answer

The kinetic energy gained by an electron accelerated through a potential difference V is given by:

K = qV

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

For an electron, q = -1.6 x 10^-19 C.

Substituting this value and the given potential difference of 60 000 V, we get:

K = (-1.6 x 10^-19 C) x (60 000 V) = -9.6 x 10^-15 J

This value can be converted to electron volts (eV) using the conversion factor 1 eV = 1.6 x 10^-19 J:

K = (-9.6 x 10^-15 J) / (1.6 x 10^-19 J/eV) = -60 keV

Note that the negative sign indicates that the electron has lost potential energy and gained kinetic energy. To obtain the absolute value of the kinetic energy, we ignore the negative sign:

|K| = 60 keV

Therefore, the kinetic energy of each electron in the x-ray machine is 60 keV. The answer choice that corresponds to this is D.

Electrons in an X-Ray Machine Are Accelerated from Rest Through