Through what potential difference would an electron initially at rest need to be accelerated to have its total energy be double its rest energy? (m_e = 9.11 x 10^-31 kg,c = 3.00 x 10⁸ m/s,and q_e = 1.6 x 10^-19 C) A)1.6 x 10^-19 V B)2.6 x 10⁵ V C)5.1 x 10⁵ V D)1.0 x 10⁶ V

Question

Quizplus · Accepted Answer

The total energy of a particle with mass m and charge q accelerated through a potential difference V is given by:
E = (1/2)mv^2 + qV
For an electron initially at rest, the first term on the right-hand side of the equation is zero, so we have:
E = qV
To find the potential difference required for the electron to have double its rest energy, we set E equal to 2mc^2, where c is the speed of light:
2mc^2 = qV
Solving for V, we get:
V = (2mc^2)/q
Substituting the given values, we get:
V = (2 x 9.11 x 10^-31 kg x (3.00 x 10^8 m/s)^2) / (1.6 x 10^-19 C)
V ≈ 5.1 x 10^15 V
Therefore, the answer is (C).

Through What Potential Difference Would an Electron Initially at Rest