`M_p` denotes the mass of a proton and `M_n` that of a neutron. A given nucleus, of binding energy `B`, contains `Z` protons and `N` neutrons. The mass `M(N,Z)` of the nucleus is given by.

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

A

Explanation

(a) Binding energy of a nucleus containing `N` neutrons and `Z` protons is
`BR[NM_n + ZM_p - M(A, Z)] c^2`
`rArr (BE)/(c^2) = NM_n + ZM_p - M(A, Z)`
`rArr (BE)/(c^2) = (A - Z) M_n + ZM_p - M(A)`
`(as N = A - Z)`
`rArr M(A,Z) = ZM_p + (A - Z) M_n - BE//c^2`
Density `(A)/((4)/(3) pi R^3)`
`:. rho _(A_1) : rho_(A_2) = (1)/((4)/(3) pi R_0^3 .1^3) = (3)/((4)/(3) pi R_0^3(3^(1//3))^3)`
Their nuclear densities will be the same.