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Question: Answered & Verified by Expert
In one model of the electron, the electron of mass $m_{c}$ is thought to be a uniformly charged shell of radius $R$ and total charge e, whose electrostatic energy $E$ is equivalent to its mass $m_{c}$ via Einstein's mass energy relation $E=$$\mathrm{m}_{\mathrm{e}} \mathrm{c}^{2} .$ In this model, $\mathrm{R}$ is approximately $\left(\mathrm{m}_{\mathrm{c}}=9.1 \times 10^{-31} \mathrm{~kg}, \mathrm{c}=3 \times 10^{8} \mathrm{~ms}^{-1}, 1 / 4 \pi \varepsilon_{0}=9 \times 10^{9}\right.$ Farad $\mathrm{m}^{-1}$, magnitude of the electron charge $\left.=1.6 \times 10^{-19} \mathrm{C}\right)-$
PhysicsNuclear PhysicsKVPYKVPY 2012 (SB/SX)
Options:
  • A $1.4 \times 10^{-15} \mathrm{~m}$
  • B $5.3 \times 10^{-11} \mathrm{~m}$
  • C $2 \times 10^{-13} \mathrm{~m}$
  • D $2.8 \times 10^{-35} \mathrm{~m}$
Solution:
1503 Upvotes Verified Answer
The correct answer is: $1.4 \times 10^{-15} \mathrm{~m}$
$\frac{\mathrm{e}^{2}}{8 \pi \varepsilon_{0} \mathrm{R}}=\mathrm{m}_{\mathrm{e}} \mathrm{c}^{2}$
solving for $\mathrm{R}$

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