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

Explanation

To find the mass \( M(N, Z) \) of a nucleus containing \( Z \) protons and \( N \) neutrons, we can use the concept of binding energy \( B \). The binding energy is the energy required to disassemble a nucleus into its constituent protons and neutrons. The relationship between the binding energy and the mass of the nucleus can be expressed as follows:

1. **Write the binding energy equation**:
The binding energy \( B \) can be expressed in terms of the masses of the protons and neutrons and the mass of the nucleus:
\[ B = Z M_p + N M_n - M(N, Z) c^2 \]
where:
- \( Z \) is the number of protons,
- \( M_p \) is the mass of a proton,
- \( N \) is the number of neutrons,
- \( M_n \) is the mass of a neutron,
- \( M(N, Z) \) is the mass of the nucleus,
- \( c \) is the speed of light.

2. **Rearrange the equation to solve for the mass of the nucleus**:
We can rearrange the equation to isolate \( M(N, Z) \):
\[ M(N, Z) c^2 = Z M_p + N M_n - B \]
Dividing both sides by \( c^2 \):
\[ M(N, Z) = \frac{Z M_p + N M_n - B}{c^2} \]

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