If an electron,initially at rest,is accelerated through a potential difference of 180 kV,the relativistic mass of the electron is A)12.3 $\times$ 10^-31 kg B)9.11 $\times$ 10^-31 kg C)16.2 $\times$ 10^-31 kg D)5.90 $\times$ 10^-31 kg E)infinite

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When an electron is accelerated through a potential difference, its kinetic energy increases, which according to the theory of relativity, results in an increase in its mass. The relativistic mass of the electron can be calculated using the equation $E = mc^2$, where $E$ is the energy gained by the electron, $m$ is the relativistic mass increase, and $c$ is the speed of light. The energy gained by the electron can be calculated from the potential difference (V) it is accelerated through, using the equation $E = eV$, where $e$ is the charge of the electron. For a potential difference of 180 kV, the energy gained is significant, and when calculated correctly, it leads to an increase in the electron's mass, which matches the value given in option A. This calculation takes into account relativistic effects, which are significant at high velocities comparable to the speed of light.

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