Answer:
0.572 MeV
2.467 MeV
Explanation:
c = Speed of light = [tex]3\times 10^8\ m/s[/tex]
m = Mass of electron = [tex]9.11\times 10^{-31}\ kg[/tex]
v = Final velocity
u = Initial velocity
Kinetic energy is given by
[tex]E=mc^2\left[\dfrac{1}{\sqrt{1-\dfrac{v^2}{c^2}}}-\dfrac{1}{\sqrt{1-\dfrac{u^2}{c^2}}}\right]\\\Rightarrow E=9.11\times 10^{-31}\times (3\times 10^8)^2\left[\dfrac{1}{\sqrt{1-\dfrac{0.898^2c^2}{c^2}}}-\dfrac{1}{\sqrt{1-\dfrac{0.5^2c^2}{c^2}}}\right]\\\Rightarrow E=9.16689\times 10^{-14}\ J\\\Rightarrow E=\dfrac{9.16689\times 10^{-14}}{1.6\times 10^{-13}}\\\Rightarrow E=0.572\ MeV[/tex]
The energy required is 0.572 MeV
[tex]E=mc^2\left[\dfrac{1}{\sqrt{1-\dfrac{v^2}{c^2}}}-\dfrac{1}{\sqrt{1-\dfrac{u^2}{c^2}}}\right]\\\Rightarrow E=9.11\times 10^{-31}\times (3\times 10^8)^2\left[\dfrac{1}{\sqrt{1-\dfrac{0.99^2c^2}{c^2}}}-\dfrac{1}{\sqrt{1-\dfrac{0.898^2c^2}{c^2}}}\right]\\\Rightarrow E=3.94869\times 10^{-13}\ J\\\Rightarrow E=\dfrac{3.94869\times 10^{-13}}{1.6\times 10^{-13}}\\\Rightarrow E=2.467\ MeV[/tex]
The energy required is 2.467 MeV
