If `M(A,Z)`, `M_(p)and M_(n)` denote the masses of the nucleus `._(Z)X^(A)`, proton and neutron respectively in units of U (where`1U=931MeV//c^(2)`) and B.E. represents its B.E. in MeV, then

Options

A. `M(A,Z)=ZM_(p)+(A-Z)M_(n)+BE//c^(2)`
B. `M(A,Z)=ZM_(p)+(A-Z)M_(n)+BE`
C. `M(A,Z)=ZM_(p)+(A-Z)M_(n)-BE`
D. `M(A,Z)=ZM_(p)+(A-Z)M_(n)+BE//c^(2)`

Answer

B

Explanation

The radius of a nucleus is given by the relation,
`r=r_(0)(A)^(1//3)" (key concept)"`
for `Os^(189),A_(1)=189,r_(1)=r` (say)
thus, using `r_(2)=(r)/(3)`, we have
`(r_(1))/(r_(2))=((A_(1))/(A_(2)))^(1//3) implies 3=((189)/(A_(2)))^(1//3)`
`implies 27=(189)/(A_(2))implies A_(2)=7`
Thus, the answer is `Li^7`.