Calculate the disintegration energy Q for the fission of `""^(52)Cr` into two equal fragments. The masses you will need are
`""^(52)Cr " "51.94051u" """^(26)Mg" "25.98259u`

Answer

To calculate the disintegration energy \( Q \) for the fission of \( {}^{52}\text{Cr} \) into two equal fragments of \( {}^{26}\text{Mg} \), we can follow these steps:

### Step 1: Identify the masses involved
We have:
- Mass of \( {}^{52}\text{Cr} = 51.94051 \, u \)
- Mass of \( {}^{26}\text{Mg} = 25.98259 \, u \)

### Step 2: Write the reaction equation
The fission can be represented as:
\[ {}^{52}\text{Cr} \rightarrow 2 \, {}^{26}\text{Mg} \]

### Step 3: Calculate the total mass of the products
Since we have two \( {}^{26}\text{Mg} \) nuclei, the total mass of the products is:
\[ \text{Total mass of products} = 2 \times \text{mass of } {}^{26}\text{Mg} = 2 \times 25.98259 \, u = 51.96518 \, u \]

### Step 4: Calculate the mass defect
The mass defect \( \Delta M \) is given by the difference between the mass of the reactants and the total mass of the products:
\[ \Delta M = \text{mass of } {}^{52}\text{Cr} - \text{total mass of products} \]
Substituting the values:
\[ \Delta M = 51.94051 \, u - 51.96518 \, u = -0.02467 \, u \]

### Step 5: Convert mass defect to energy
Using Einstein's equation \( E = \Delta M c^2 \), we convert the mass defect to energy. The conversion factor is \( 931.5 \, \text{MeV/u} \):
\[ Q = \Delta M \times 931.5 \, \text{MeV/u} \]
Substituting the mass defect:
\[ Q = -0.02467 \, u \times 931.5 \, \text{MeV/u} = -23.0 \, \text{MeV} \]

### Final Answer
The disintegration energy \( Q \) for the fission of \( {}^{52}\text{Cr} \) into two equal fragments is:
\[ Q = -23.0 \, \text{MeV} \]

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