The masses of neutron, proton and deuteron in amu are 1.00893, 1.00813 and 2.01473 respectively. The packing fraction of the deuteron in amu is

Options

A. `11.65 xx 10^(-4)`
B. `23.5 xx 10^(-4)`
C. `33.5 xx 10^(-4)`
D. `47.15 xx 10^(-4)`

Answer

To find the packing fraction of the deuteron, we will follow these steps:

### Step 1: Understand the components of the deuteron
The deuteron consists of one proton and one neutron. We need to find the total mass of these components.

### Step 2: Calculate the total mass of the deuteron
The mass of the proton (m_p) is 1.00813 amu, and the mass of the neutron (m_n) is 1.00893 amu. Therefore, the total mass (m_total) of the deuteron can be calculated as:
\[ m_{\text{total}} = m_p + m_n = 1.00813 \, \text{amu} + 1.00893 \, \text{amu} \]
\[ m_{\text{total}} = 2.01706 \, \text{amu} \]

### Step 3: Determine the mass of the deuteron
The mass of the deuteron (m_d) is given as 2.01473 amu.

### Step 4: Calculate the packing fraction
The packing fraction (PF) is defined as:
\[ \text{Packing Fraction} = \frac{\text{Total mass of nucleons} - \text{mass of the nucleus}}{\text{mass number}} \]
For the deuteron, the mass number (A) is 2 (since it contains one proton and one neutron). Thus, we can write:
\[ \text{Packing Fraction} = \frac{(m_p + m_n) - m_d}{A} \]
Substituting the values we have:
\[ \text{Packing Fraction} = \frac{(2.01706 \, \text{amu}) - (2.01473 \, \text{amu})}{2} \]
\[ \text{Packing Fraction} = \frac{0.00233 \, \text{amu}}{2} \]
\[ \text{Packing Fraction} = 0.001165 \, \text{amu} \]

### Final Answer
The packing fraction of the deuteron is approximately **0.001165 amu**.

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