Find the mass, the kinetic energy and the momentum of an electron moving at 0.8c.

Explanation

Given ` m_0 = 9.1 xx 10^(-31) `
`v = 0.8 c `
(a) `m' = M_0 / (sqrt 1 - v^(2) / c^(2))`
` = 9.1 xx 10^(-31)/ (sqrt 1 - 0.64 c^(2) / c^(2) `
` = 9.1 xx 10^(31) / 0.6 `
` = 15.16 xx 10^(-31) Kg `
` = 15.2 xx 10^(31) Kg `
` = 15.2 xx 10^(-31) Kg`
(b) K.E. of the electron
` = m' c^(2) - m_0 c^(2)`
` (m' - m_0 ) c^(2) `
` = (15.2 xx 10^(-31) - 9.1 xx 10^(-31) ) (3 xx 10^(8))^(2) `
`( 15.2 - 9.1 ) xx 9 xx 10^(-31) xx 10^(16) J`
` = 54 .6 xx 10^(-15) J = 5.46 xx 10^(-14) J `
` 5.5 xx 10^(-14) J`
(c ) Momentum of the given electron
` = Apparent mass xx given velocity `
` = 15.2 xx 10^(-31) kg xx 0.8 xx 3 xx 10^(8) m / s `
`= 36.48 xx 10^(-23) Kg m / s `
3.65 xx 10^(-22) kgm / s `