The energy equivalent to 1 kg of matter is :

Options

A. `9xx10^(16)J`
B. `9xx10^(16)" erg"`
C. 1 J
D. 100 J

Answer

To find the energy equivalent of 1 kg of matter, we will use the mass-energy equivalence formula given by Einstein:

\[ E = mc^2 \]

Where:
- \( E \) is the energy equivalent,
- \( m \) is the mass,
- \( c \) is the speed of light in vacuum.

### Step 1: Identify the values
- Given mass \( m = 1 \, \text{kg} \)
- The speed of light \( c = 3 \times 10^8 \, \text{m/s} \)

### Step 2: Substitute the values into the formula
Now we will substitute the values into the equation:

\[ E = 1 \times (3 \times 10^8)^2 \]

### Step 3: Calculate \( c^2 \)
First, we calculate \( (3 \times 10^8)^2 \):

\[ (3 \times 10^8)^2 = 3^2 \times (10^8)^2 = 9 \times 10^{16} \]

### Step 4: Calculate \( E \)
Now substituting back into the energy equation:

\[ E = 1 \times 9 \times 10^{16} = 9 \times 10^{16} \, \text{Joules} \]

### Conclusion
Thus, the energy equivalent to 1 kg of matter is:

\[ E = 9 \times 10^{16} \, \text{Joules} \]

### Final Answer
The correct answer is option 1: \( 9 \times 10^{16} \, \text{Joules} \).

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