If the masses of the nucleus, proton and neutron are denoted by `M(A,Z),M_(p)` and `M_(n)`, u(where `1u=931.MVc^(-2)`)and BE represents it's binding energy in MeV, then choose the correct relation for the given nucleus.

Options

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

Answer

A

Explanation

Binding energy of a nucleus containing N neutrons and Z protons is N.
`BE=[NM_(n)+ZM_(p)-M(A,Z)]c^(2)`
`implies(BE)/(c^(2))=NM_(n)+ZM_(p)-M(A,Z)`
`implies(BE)/(c^(2))=(A-Z)M_(n)+ZM_(p)`
`-M(A,Z)("as"N=A-Z)`
`impliesM(A,Z)=ZM_(p)+(A-Z)M_(n)`
`-BEc^(-2)`