The rest mass of an electron is `9.1 xx10^(-31)` kg. Its kinetic energy when it moves with a speed of `2.4xx10^(8)` m/s is

Options

A. `5.45xx10^(-14) J`
B. `54.36xx10^(-14) J`
C. `56.43xx10^(-14) J`
D. `53.46xx10^(-14)J`

Answer

A

Explanation

The mass of electron is given by,
`m=m_(0)/sqrt(1-v^(2)/c^(2))=(9.1xx10^(-31))/sqrt(1-((2.4xx10^(8))/(3xx10^(8)))^(2))`
`=15.16xx10^(-31) kg`
The total energy of electron is given by,
`E=mc^(2)`
`=15.16xx10^(-31) xx9xx10^(16)`
`=136.44xx10^(-15) J`
Now, rest mass energy of electron is,
`m_(0)c^(2)=9.1xx10^(-31)xx9xx10^(16)`
`=81.9xx10^(-15)J`
Thus, K.E. of electron is given by,
`E_(k)=E-m_(0) c^(2)`
`=136.44xx10^(-15)-81.9xx10^(-15)`
`=5.454xx10^(-14) J`
`~~5.45xx10^(-14) J`