Solution
= Solution
Applying the same <work-energy theorem> at the higher pair of <speeds> gives
$$
\boxed{W_b=511\left(\frac1{\sqrt{1-0.99^2}}-\frac1{\sqrt{1-0.98^2}}\right)\mathrm{keV}\simeq1055\,\mathrm{keV}\simeq1.689\times10^{-13}\,\mathrm J.}
$$
The identical increment $0.01c$ now needs about two thousand times as much <work>. The growth follows from the rapidly increasing <Lorentz factor> near the <speed of light>.