= Solution
The external <work> equals the change in <relativistic kinetic energy>, $W=m_ec^2(\gamma_f-\gamma_i)$. With $m_ec^2=511\,\mathrm{keV}$,
$$
\boxed{W_a=511\left(\frac1{\sqrt{1-0.11^2}}-\frac1{\sqrt{1-0.10^2}}\right)\mathrm{keV}\simeq0.5456\,\mathrm{keV}\simeq8.742\times10^{-17}\,\mathrm J.}
$$
The <rest energy> cancels between endpoints. At these <speeds>, the nonrelativistic estimate $\tfrac12m_e c^2(0.11^2-0.10^2)=0.53655\,\mathrm{keV}$ is close but slightly smaller.
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