With what velocity should an `alpha ` paricle travel towards the nucleus of a copper atom so as to arrive at a distance `10^(-13)m` from the nucleus of the copper atom?

Answer

A

Explanation

Potential energy of the `alpha` particle at a distance `10^(-13)m ` from the nucless of a copper atom is
`V = (-Z_(1)Z_(2)e^(2))/((4pi epsilon_(0))r)`
`= (-(29)(4)(1.6 xx 10^(-19)C)^(2))/((4)(3.14)(8.85 xx 10^(-12) J^(-1)C^(2)m^(-1))(10^(-13)m))`
`= - 2.67 xx 10^(-13) J`
Velocity at which `alpha` particle should move is
`v = sqrt((2|v|)/(m))`
`= [((2)(2.67 xx 10^(-13)J))/((4.0 xx 10^(-3) kg mol^(-1))(6.02 xx 10^(23)mol^(-1)))]^((1)/(2))`
`= 8.97 xx 10^(6) m s^(-1)`