An electron has a momentum of 0.86 MeV/c. The fraction of the electron's kinetic energy compared to its total energy is

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Quizplus · Accepted Answer

The fraction of the electron's kinetic energy (KE) compared to its total energy (E) can be calculated using the formula for relativistic energy and momentum. The total energy E is given by $E = \sqrt{(pc)^2 + (m_0c^2)^2}$, where $p$ is the momentum, $c$ is the speed of light, and $m_0$ is the rest mass of the electron. The kinetic energy (KE) is the total energy minus the rest energy ($m_0c^2$). The fraction is then $\frac{KE}{E} = \frac{E - m_0c^2}{E}$.Given that the momentum $p = 0.86 \, \text{MeV/c}$ and the rest mass energy of an electron $m_0c^2 = 0.511 \, \text{MeV}$, we can calculate the total energy $E$ and then find the fraction.First, calculate the total energy:$$E = \sqrt{(0.86)^2 + (0.511)^2} = \sqrt{0.7396 + 0.261121} = \sqrt{1.000721} \, \text{MeV} \approx 1.00036 \, \text{MeV}$$Then, calculate the kinetic energy:$$KE = E - m_0c^2 = 1.00036 - 0.511 = 0.48936 \, \text{MeV}$$Finally, calculate the fraction:$$\frac{KE}{E} = \frac{0.48936}{1.00036} \approx 0.489 \text{ or } 48.9\%$$This value is closest to option B) 49%.

An Electron Has a Momentum of 0