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# An electron has a total energy of 2MeV.Calculate the effective mass of the electron in Kg and its speed .Assume rest mass of electron 0.511MeV

$\begin{array}{1 1}(a)\;23.6\times 10^{-31}Kg,3.9\times 10^{10}cm/s\\(b)\;35.6\times 10^{-31}Kg,2.9\times 10^{10}cm/s\\(c)\;21.6\times 10^{-31}Kg,1.9\times 10^{10}cm/s\\(d)\;23.6\times 10^{-19}Kg,2.9\times 10^{5}cm/s\end{array}$

Mass of electron in Motion $=\large\frac{2}{931}$amu
$\Rightarrow \large\frac{2}{931}$$\times 1.66\times 10^{-27}kg$
$1amu=931MeV$
$\Rightarrow 35.6\times 10^{-31}kg$
Also $M_e=\large\frac{m_e^0}{\sqrt{1-\big(\Large\frac{v}{c}\big)^2}}$
$35.6\times 10^{-31}=\large\frac{\Large\frac{0.511}{931}\times 1.66\times 10^{-27}}{\sqrt{1-\big[\large\frac{u}{3\times 10^{10}}\big]^2}}$
$u=2.9\times 10^{10}cm/s$
Hence (b) is the correct answer.

+1 vote