Calculate the impact parameter of a 5 MeV particle scattered by `90^(@)`, when it approach a gold nucleus (Z=79).

Options

A. `1.5 times 10^(-14)`m
B. `2.27 times 10^(-14)m`
C. `3 times 10^(-14)m`
D. `3.37 times 10^(-17)m`

Answer

B

Explanation

Impact parameter `b=1/(4piepsilon_(0))(Ze^(2)cot(theta/2))/K`
where, K is the K.E. of the approaching particle.
In this case `1/(4piepsilon_(0))=9 times 10^(9), Z=79, e=1.6 times 10^(-19)`
K = 5 `MeV=5 times 10^(6) times 1.6 times 10^(-19)`
`" "=(9 times 79 times 1.6 times cot45^(@) times 10)/5`
`therefore b=227 times 10^(-16)=2.27 times 10^(-14)m`
`therefore` The impact parameter (b) `=2.27 times 10^(-14)` m.