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Question: An electron has a total energy of 2 MeV. Calculate the effective mass of the electron in kg and its ...

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

A

2.9×1082.9 \times 10^{8}

B

8.01×1088.01 \times 10^{8}

C

9.652×1089.652 \times 10^{8}

D

None

Answer

2.9×1082.9 \times 10^{8}

Explanation

Solution

Mass of electron in motion =2931amu= \frac{2}{931}amu (1 amu = 931 MeV)

=2931×1.66×1027kg=3.56×1030kg= \frac{2}{931} \times 1.66 \times 10^{- 27}kg = 3.56 \times 10^{- 30}kg (1)

amu=1.66×1027kgamu = 1.66 \times 10^{- 27}kg)

Let the speed of the electron be u.

m=m1(u/c)2m^{'} = \frac{m}{\sqrt{1 - (u/c)^{2}}} or

3.56×1030=0.511931×1.66×10271(u3×108)2=0.911×10301(u3×108)23.56 \times 10^{- 30} = \frac{\frac{0.511}{931} \times 1.66 \times 10^{- 27}}{\sqrt{1 - \left( \frac{u}{3 \times 10^{8}} \right)^{2}}} = \frac{0.911 \times 10^{- 30}}{\sqrt{1 - \left( \frac{u}{3 \times 10^{8}} \right)^{2}}}or 1(u3×108)2=0.065481 - \left( \frac{u}{3 \times 10^{8}} \right)^{2} = 0.06548 or u2=9×1016×0.93452u^{2} = 9 \times 10^{16} \times 0.93452 or u=2.9×108mu = 2.9 \times 10^{8}m