In the mass of `""^(228)Thto""^(224)Ra+alpha` : Atomic mass of `""^(228)Th` is 228.0287u `""^(228)Ra` is `224.0202:""^(4)He` is 4.0026u. What is Q value of reaction (approximately)

Options

A. 5.49 MeV
B. 4.95 MeV
C. 5.9 MeV
D. 7.36 MeV

Answer

To find the Q value of the nuclear reaction \( ^{228}\text{Th} \rightarrow ^{224}\text{Ra} + \alpha \), we will follow these steps:

### Step 1: Identify the masses of the reactants and products
- The mass of \( ^{228}\text{Th} \) is given as \( 228.0287 \, \text{u} \).
- The mass of \( ^{224}\text{Ra} \) is given as \( 224.0202 \, \text{u} \).
- The mass of \( \alpha \) (which is equivalent to \( ^{4}\text{He} \)) is given as \( 4.0026 \, \text{u} \).

### Step 2: Calculate the total mass of the products
The total mass of the products is the sum of the masses of \( ^{224}\text{Ra} \) and \( \alpha \):
\[ \text{Total mass of products} = \text{mass of } ^{224}\text{Ra} + \text{mass of } \alpha \]
\[ = 224.0202 \, \text{u} + 4.0026 \, \text{u} = 228.0228 \, \text{u} \]

### Step 3: Calculate the mass defect (\( \Delta m \))
The mass defect is calculated as the difference between the mass of the reactant and the total mass of the products:
\[ \Delta m = \text{mass of } ^{228}\text{Th} - \text{Total mass of products} \]
\[ = 228.0287 \, \text{u} - 228.0228 \, \text{u} = 0.0059 \, \text{u} \]

### Step 4: Calculate the Q value
The Q value can be calculated using the formula:
\[ Q = \Delta m \times c^2 \]
In nuclear physics, this is often expressed in terms of MeV using the conversion factor \( 1 \, \text{u} \approx 931.5 \, \text{MeV} \):
\[ Q = \Delta m \times 931.5 \, \text{MeV} \]
Substituting the value of \( \Delta m \):
\[ Q = 0.0059 \, \text{u} \times 931.5 \, \text{MeV} \approx 5.49 \, \text{MeV} \]

### Final Answer
The Q value of the reaction is approximately \( 5.49 \, \text{MeV} \).

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