`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(N,Z)= NM_n + ZM_p - Bc^2`
B. `M(N,Z) = NM_n + ZM_p + Bc^2`
C. `M(N,Z) = NM_n + ZM_p - B//c^2`
D. `M(N,Z) = NM,, + ZM_p + B//c^2`

Explanation

To find the mass \( M(N, Z) \) of a nucleus containing \( Z \) protons and \( N \) neutrons with a binding energy \( B \), we can follow these steps:

### Step 1: Understand the Binding Energy
The binding energy \( B \) of a nucleus is the energy required to disassemble the nucleus into its constituent protons and neutrons. It can be expressed in terms of the mass of the nucleus and the masses of the individual nucleons (protons and neutrons).

### Step 2: Write the Mass of Constituent Particles
The total mass of the individual nucleons (protons and neutrons) in the nucleus can be calculated as:
\[ \text{Total mass of nucleons} = Z \cdot M_p + N \cdot M_n \]
where \( M_p \) is the mass of a proton and \( M_n \) is the mass of a neutron.

### Step 3: Relate Binding Energy to Mass
The binding energy \( B \) can be related to the mass defect (the difference between the mass of the individual nucleons and the mass of the nucleus) by the equation:
\[ B = \text{(mass of nucleons)} - \text{(mass of nucleus)} \cdot c^2 \]
Rearranging this gives us:
\[ B = (Z \cdot M_p + N \cdot M_n - M(N, Z)) \cdot c^2 \]

### Step 4: Solve for the Mass of the Nucleus
Rearranging the equation for \( M(N, Z) \):
\[ M(N, Z) = Z \cdot M_p + N \cdot M_n - \frac{B}{c^2} \]

### Final Expression
Thus, the mass of the nucleus can be expressed as:
\[ M(N, Z) = Z \cdot M_p + N \cdot M_n - \frac{B}{c^2} \]