The binding energy of `._(10)Ne^(20)` is 160.6 MeV. Find its atomic mass. Take mass of proton =1.007825 u and mass of neutron =1.008665 u.

Explanation

To find the atomic mass of \( _{10}^{20}\text{Ne} \) given its binding energy, we can follow these steps:

### Step 1: Understand the relationship between binding energy and mass defect
The binding energy (BE) of a nucleus is related to the mass defect (\( \Delta m \)) by the equation:
\[ BE = \Delta m \cdot c^2 \]
where \( c \) is the speed of light. In atomic mass units (u), we can convert binding energy from MeV to atomic mass units using the conversion factor \( 1 \text{ MeV} \approx 1.073 \times 10^{-9} \text{ u} \).

### Step 2: Convert binding energy to mass defect
Given:
- Binding energy \( BE = 160.6 \text{ MeV} \)

Using the conversion:
\[ \Delta m = \frac{BE}{931.5 \text{ MeV/u}} = \frac{160.6 \text{ MeV}}{931.5 \text{ MeV/u}} \approx 0.17250 \text{ u} \]

### Step 3: Calculate the total mass of protons and neutrons
For \( _{10}^{20}\text{Ne} \):
- Number of protons \( Z = 10 \)
- Number of neutrons \( N = 20 - 10 = 10 \)

The total mass of protons and neutrons can be calculated as:
\[ \text{Total mass} = (Z \cdot m_p) + (N \cdot m_n) \]
where:
- \( m_p = 1.007825 \text{ u} \) (mass of proton)
- \( m_n = 1.008665 \text{ u} \) (mass of neutron)

Calculating:
\[ \text{Total mass} = (10 \cdot 1.007825) + (10 \cdot 1.008665) \]
\[ = 10.07825 + 10.08665 = 20.1649 \text{ u} \]

### Step 4: Calculate the atomic mass of \( _{10}^{20}\text{Ne} \)
Now, we can find the atomic mass of \( _{10}^{20}\text{Ne} \) using the mass defect:
\[ m_{\text{Ne}} = \text{Total mass} - \Delta m \]
\[ m_{\text{Ne}} = 20.1649 \text{ u} - 0.17250 \text{ u} \approx 19.9924 \text{ u} \]

### Final Answer
The atomic mass of \( _{10}^{20}\text{Ne} \) is approximately **19.9924 u**.

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