Large angle scattering of `alpha-`particle led Rutherford to the discovery of atomic nucleus. It is the tiny central core of every atom in which entire positive charge of the atom is concentrated. The distance of closet approach of alpha particle from the nucleus is
`r_(theta)=((Ze)(2e))/(4pi epsilon_(theta)((1)/(2)mv^(2)))`
This distance `r_(theta)` gave him the order of size of nucleus.
Read the above passage and answer the followign question:
(i) What is the distance of closet approach of an alpha particle of energy 7.7 MeV from gold nucleus (z=79)?
(ii) What is the implication of this relation in day to day life?

Explanation

`(i) Here, `E=(1)/(2) mv^(2)=7.7MeV=7.7xx1.6xx10^(-13)J`
`Z=79` and `e=1.6xx10^(-19)C`
`therefore r_(0)=((ze)(2e))/(4piepsilon_(0)((1)/(2)mv^(2)))`
`=(2xx79(1.6xx10^(-19))^(2)xx9xx10^(9))/(7.7xx1.6xx10^(-13))`
`=3.0xx10^(-14)m=30` fermi
(ii) From this relation, we find `r_(0)prop(1)/(E(=(1)/(2)mv^(2)))`, i.e. larger the energy spent, closer your approach. same is true in day to day life. To know the inside (views/mind) of a person, you have to speed lot of energy/efforts for pentrating dep into his ming. you cannot assess the mind of a person on its face value.