The rest mass energy of an electron is 0.54 , | vedclass

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(A) Given,rest mass energy $E_0 = m_0 c^2 = 0.54 \, MeV$.Velocity of the electron $v = 0.8 \, c$.The relativistic mass $m$ is given by $m = \frac{m_0}

Vedclass · Accepted Answer

$0.36$

Vedclass · Answer

(A) Given,rest mass energy $E_0 = m_0 c^2 = 0.54 \, MeV$.Velocity of the electron $v = 0.8 \, c$.The relativistic mass $m$ is given by $m = \frac{m_0}{\sqrt{1 - \frac{v^2}{c^2}}}$.Substituting $v = 0.8 \, c$:$m = \frac{m_0}{\sqrt{1 - (0.8)^2}} = \frac{m_0}{\sqrt{1 - 0.64}} = \frac{m_0}{\sqrt{0.36}} = \frac{m_0}{0.6}$.The total energy $E = mc^2 = \frac{m_0 c^2}{0.6}$.Substituting $m_0 c^2 = 0.54 \, MeV$:$E = \frac{0.54}{0.6} = 0.9 \, MeV$.The kinetic energy $K.E.$ is given by $K.E. = E - E_0$.$K.E. = 0.9 \, MeV - 0.54 \, MeV = 0.36 \, MeV$.

The rest mass energy of an electron is $0.54 \, MeV$. If the velocity of the electron is $0.8 \, c$,then the kinetic energy $(K.E.)$ of the electron is .......... $MeV$.

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