Question

an electron whose rest mass is 9.11x10^-31 kg moves with a speed of 0.8c .what its kinetic energy

Answer 1

there fore,the kinetic energy of electron =
$26.208 \times {10}^{ - 15}$

Answer 2

The speed of the electron is given as v = 0.8 c

The rest mass of the electron $m_{0}=\ 9.11\times 10^-31\ kg$

As per Einstein's relativistic theory , the mass of a body increases relatively when speed is comparable to the velocity of light.

Let the mass of the electron in motion is denoted as m .

Mathematically it can be written as -

                                  $m=\frac{m_{0}} {\sqrt{1-\frac{v^2}{c^2}}}$

                                            $=\frac{9.11\times 10^-31\ kg}{\sqrt{1-\frac{(0.8c)^2}{c^2}}}$

                                           $=\frac{9.11\times 10^-31\ kg}{0.6}$

                                           $=1.52\times 10^-30\ kg$

Now we have to calculate the kinetic energy of the electron

The kinetic energy of the electron is -

              Kinetic energy K.E = $\frac{1}{2} mv^2$

                                             = $\frac{1}{2} 1.52\times 10^-30\times (0.8c)^2\ Joule$

                                             =$\frac{1}{2}\times1.52\times 10^-30\times0.64\times (3\times 10^8)^2\ Joule$

                                            = $4.38\times 10^-14\ Joule$    [ans]