An electron, initially at rest, is accelerated through a potential difference of 2.5 MeV, thereby increasing its total energy by 2.5 MeV. The mass of the electron is

Question

Quizplus · Accepted Answer

The correct answer is A because the kinetic energy of the electron is equal to the potential difference through which it is accelerated. The kinetic energy of an electron is given by the equation:$$K = eV$$where:* K is the kinetic energy in joules* e is the charge of the electron in coulombs* V is the potential difference in voltsIn this case, the potential difference is 2.5 MeV, which is equal to 2.5 x 10^6 volts. The charge of the electron is -1.602 x 10^-19 coulombs. Therefore, the kinetic energy of the electron is:$$K = (-1.602 x 10^-19 C)(2.5 x 10^6 V) = -4.005 x 10^-13 J$$The total energy of the electron is equal to its kinetic energy plus its rest energy. The rest energy of an electron is given by the equation:$$E_0 = mc^2$$where:* E_0 is the rest energy in joules* m is the mass of the electron in kilograms* c is the speed of light in meters per secondThe speed of light is 2.998 x 10^8 meters per second. The mass of the electron is 9.109 x 10^-31 kilograms. Therefore, the rest energy of the electron is:$$E_0 = (9.109 x 10^-31 kg)(2.998 x 10^8 m/s)^2 = 8.187 x 10^-14 J$$The total energy of the electron is:$$E = K + E_0 = -4.005 x 10^-13 J + 8.187 x 10^-14 J = -3.186 x 10^-13 J$$The negative sign indicates that the electron is bound to the atom. The mass of the electron is:$$m = \frac{E}{c^2} = \frac{-3.186 x 10^-13 J}{(2.998 x 10^8 m/s)^2} = 5.44 x 10^-30 kg$$Therefore, the mass of the electron is 5.44 x 10^-30 kg, which is closest to choice A.

An Electron, Initially at Rest, Is Accelerated Through a Potential 5.4×10−30 kg5.4 \times 10 ^ { - 30 } \mathrm {~kg}5.4×10−30 kg

An Electron, Initially at Rest, Is Accelerated Through a Potential $5.4 \times 10 ^ { - 30 } \mathrm {~kg}$