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. `1.5 xx 10^6`
B. `2.5 xx 10^6`
C. `3 xx 10^6`
D. `7.5 xx 10^6`

Explanation

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

### Step 1: Convert mass defect from grams to kilograms
Given:
- Mass defect, Δm = 0.3 grams

To convert grams to kilograms, we use the conversion factor:
\[ 1 \text{ gram} = 0.001 \text{ kilograms} \]
Thus,
\[ \Delta m = 0.3 \text{ grams} = \frac{0.3}{1000} = 0.0003 \text{ kg} \]

### Step 2: Calculate the energy using Einstein's equation
Einstein's mass-energy equivalence principle states:
\[ E = \Delta m \cdot c^2 \]
Where:
- \( c \) (speed of light) = \( 3 \times 10^8 \text{ m/s} \)

Now, we can calculate \( c^2 \):
\[ c^2 = (3 \times 10^8)^2 = 9 \times 10^{16} \text{ m}^2/\text{s}^2 \]

Now, substitute the values into the energy equation:
\[ E = 0.0003 \text{ kg} \cdot 9 \times 10^{16} \text{ m}^2/\text{s}^2 \]
\[ E = 0.0003 \times 9 \times 10^{16} = 2.7 \times 10^{13} \text{ joules} \]

### Step 3: Convert energy from joules to kilowatt hours
To convert joules to kilowatt hours, we use the conversion factor:
\[ 1 \text{ kilowatt hour} = 3.6 \times 10^6 \text{ joules} \]

Now, we can convert the energy:
\[ E \text{ (in kWh)} = \frac{E \text{ (in joules)}}{3.6 \times 10^6} \]
Substituting the value of \( E \):
\[ E \text{ (in kWh)} = \frac{2.7 \times 10^{13}}{3.6 \times 10^6} \]
Calculating this gives:
\[ E \text{ (in kWh)} = 7.5 \times 10^6 \text{ kWh} \]

### Final Answer
The amount of energy liberated in kilowatt hours is:
\[ 7.5 \times 10^6 \text{ kWh} \]

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