Energy of 1g Uranium is equal to

Options

A. `9.0 xx 10^(13)`J
B. `9.0 xx 10^(19)J`
C. `3.0 xx 10^(16) J`
D. `3.0 xx 10^(17)J`

Explanation

To find the energy of 1 gram of uranium using Einstein's equation, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Equation**: We will use Einstein's mass-energy equivalence formula:
\[ E = mc^2 \]
where \(E\) is the energy, \(m\) is the mass, and \(c\) is the speed of light.

2. **Convert Mass to Kilograms**: The mass of uranium is given as 1 gram. We need to convert this into kilograms because the standard unit of mass in the International System of Units (SI) is kilograms.
\[ m = 1 \text{ gram} = 1 \times 10^{-3} \text{ kg} \]

3. **Use the Speed of Light**: The speed of light (\(c\)) is a constant:
\[ c = 3 \times 10^8 \text{ m/s} \]

4. **Substitute Values into the Equation**: Now we can substitute the values of \(m\) and \(c\) into the equation \(E = mc^2\):
\[ E = (1 \times 10^{-3} \text{ kg}) \times (3 \times 10^8 \text{ m/s})^2 \]

5. **Calculate \(c^2\)**: First, calculate \(c^2\):
\[ c^2 = (3 \times 10^8)^2 = 9 \times 10^{16} \text{ m}^2/\text{s}^2 \]

6. **Calculate Energy**: Now substitute \(c^2\) back into the equation for energy:
\[ E = (1 \times 10^{-3}) \times (9 \times 10^{16}) = 9 \times 10^{13} \text{ joules} \]

7. **Final Result**: Thus, the energy of 1 gram of uranium is:
\[ E = 9.0 \times 10^{13} \text{ joules} \]