The mass defect in a particular nuclear reaction is `0.3` grams. The amont of energy liberated in kilowatt hours is.
(Velocity of light `= 3 xx 10^8 m//s`).

Options

A. `1.5xx10^(6)`
B. `2.5xx10^(6)`
C. `3xx10^(6)`
D. `7.5xx10^(6)`

Answer

To solve the problem of finding the amount of energy liberated in kilowatt hours from a mass defect of 0.3 grams, we will follow these steps:

### Step 1: Convert mass defect from grams to kilograms
The mass defect given is 0.3 grams. To convert grams to kilograms, we use the conversion factor \(1 \text{ gram} = 10^{-3} \text{ kilograms}\).

\[ \text{Mass defect} = 0.3 \text{ grams} = 0.3 \times 10^{-3} \text{ kg} = 3 \times 10^{-4} \text{ kg} \]

### Step 2: Use the mass-energy equivalence formula
According to Einstein's mass-energy equivalence principle, the energy \(E\) can be calculated using the formula:

\[ E = \Delta m c^2 \]

Where:
- \(\Delta m\) is the mass defect in kilograms,
- \(c\) is the speed of light, which is \(3 \times 10^8 \text{ m/s}\).

Substituting the values:

\[ E = (3 \times 10^{-4} \text{ kg}) \times (3 \times 10^8 \text{ m/s})^2 \]

### Step 3: Calculate \(c^2\)
First, we calculate \(c^2\):

\[ c^2 = (3 \times 10^8)^2 = 9 \times 10^{16} \text{ m}^2/\text{s}^2 \]

### Step 4: Substitute \(c^2\) back into the energy equation
Now substituting \(c^2\) back into the energy equation:

\[ E = (3 \times 10^{-4}) \times (9 \times 10^{16}) = 2.7 \times 10^{13} \text{ Joules} \]

### Step 5: Convert Joules to kilowatt hours
To convert Joules to kilowatt hours, we use the conversion factor \(1 \text{ Joule} = \frac{1}{3600 \times 1000} \text{ kilowatt hours}\):

\[ E \text{ (in kWh)} = \frac{E \text{ (in Joules)}}{3600 \times 1000} \]

Substituting the value of \(E\):

\[ E \text{ (in kWh)} = \frac{2.7 \times 10^{13}}{3600 \times 1000} \]

Calculating the denominator:

\[ 3600 \times 1000 = 3.6 \times 10^6 \]

Now calculating the energy in kilowatt hours:

\[ E \text{ (in kWh)} = \frac{2.7 \times 10^{13}}{3.6 \times 10^6} \approx 7.5 \times 10^{6} \text{ kWh} \]

### Final Answer
The amount of energy liberated in kilowatt hours is approximately:

\[ \boxed{7.5 \times 10^{6} \text{ kWh}} \]

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