The rest mass of a deuteron is equivalent to an energy of `1876 MeV`, that of a proton to `939 MeV`, and that of a neutron to` 940 MeV. A deutron may disintegrate to a proton and neutron if

Options

A. emits a X-ray photon of energy 2 MeV
B. captures a X-ray photon of energy 2MeV
C. emits a X-ray photon of energy 3 MeV
D. captures a X-ray photon energy 3 MeV

Answer

To determine whether a deuteron can disintegrate into a proton and a neutron, we need to compare the rest mass energies of the particles involved. Here’s a step-by-step solution:

### Step 1: Identify the rest mass energies
- The rest mass energy of a deuteron (D) is given as \( E_D = 1876 \, \text{MeV} \).
- The rest mass energy of a proton (p) is \( E_p = 939 \, \text{MeV} \).
- The rest mass energy of a neutron (n) is \( E_n = 940 \, \text{MeV} \).

### Step 2: Calculate the total energy of the products
When a deuteron disintegrates into a proton and a neutron, the total energy of the products (proton and neutron) can be calculated as follows:
\[ E_{\text{products}} = E_p + E_n = 939 \, \text{MeV} + 940 \, \text{MeV} = 1879 \, \text{MeV} \]

### Step 3: Compare the energies
Now, we compare the energy of the deuteron with the total energy of the products:
- Energy of the deuteron: \( E_D = 1876 \, \text{MeV} \)
- Total energy of the products: \( E_{\text{products}} = 1879 \, \text{MeV} \)

### Step 4: Determine the energy difference
To find out if the disintegration can occur, we calculate the energy difference:
\[ \Delta E = E_{\text{products}} - E_D = 1879 \, \text{MeV} - 1876 \, \text{MeV} = 3 \, \text{MeV} \]

### Step 5: Conclusion
The deuteron can only disintegrate into a proton and a neutron if it can acquire an additional energy of \( 3 \, \text{MeV} \). This energy can be provided by capturing an X-ray photon of energy \( 3 \, \text{MeV} \).

Thus, the answer is that a deuteron may disintegrate to a proton and neutron if it captures an X-ray photon of energy \( 3 \, \text{MeV} \).