How much mass has to be converted into energy to produce electric power of 500 MW for one hour ?

Options

A. `2xx10^(-5)` kg
B. `1xx10^(-5)` kg
C. `3xx10^(-5)` kg
D. `4xx10^(-5)` kg

Explanation

To determine how much mass needs to be converted into energy to produce an electric power of 500 MW for one hour, we can follow these steps:

### Step 1: Calculate the total energy required
First, we need to calculate the total energy produced in one hour at a power of 500 MW.

\[ \text{Power} = 500 \text{ MW} = 500 \times 10^6 \text{ W} \]
\[ \text{Time} = 1 \text{ hour} = 3600 \text{ seconds} \]
\[ \text{Energy} = \text{Power} \times \text{Time} = 500 \times 10^6 \text{ W} \times 3600 \text{ s} \]

Calculating this gives:

\[ \text{Energy} = 500 \times 10^6 \times 3600 = 1.8 \times 10^{12} \text{ J} \]

### Step 2: Use Einstein's mass-energy equivalence
According to Einstein's mass-energy equivalence principle, the energy \(E\) is related to mass \(m\) by the equation:

\[ E = mc^2 \]

Where \(c\) is the speed of light in a vacuum, approximately \(3 \times 10^8 \text{ m/s}\).

### Step 3: Rearrange the equation to solve for mass
We can rearrange the equation to solve for mass:

\[ m = \frac{E}{c^2} \]

### Step 4: Substitute the values
Now, substituting the energy calculated in Step 1 and the speed of light into the equation:

\[ m = \frac{1.8 \times 10^{12} \text{ J}}{(3 \times 10^8 \text{ m/s})^2} \]

Calculating \(c^2\):

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

Now substituting this back into the mass equation:

\[ m = \frac{1.8 \times 10^{12}}{9 \times 10^{16}} = 2 \times 10^{-5} \text{ kg} \]

### Conclusion
The mass that needs to be converted into energy to produce 500 MW for one hour is:

\[ m = 2 \times 10^{-5} \text{ kg} \text{ or } 20 \text{ mg} \]

---