An antomic Power station has a generating capacity of `200 MW`. The energy generated in a day by this station is.

Options

A. 200 MW
B. 200 J
C. `4800xx10^(6)J`
D. `1728xx10^(10) J`

Answer

To find the energy generated by an atomic power station with a generating capacity of 200 MW in one day, we can follow these steps:

### Step 1: Understand the relationship between power, energy, and time.
Power is defined as the rate at which energy is generated or consumed. The formula relating power (P), energy (E), and time (t) is:
\[ P = \frac{E}{t} \]
From this, we can rearrange the formula to find energy:
\[ E = P \times t \]

### Step 2: Convert the power from megawatts to watts.
The power given is 200 MW. We need to convert this to watts (W):
\[ 200 \text{ MW} = 200 \times 10^6 \text{ W} \]

### Step 3: Calculate the time in seconds for one day.
One day consists of 24 hours. To convert this into seconds:
\[ t = 24 \text{ hours} \times 60 \text{ minutes/hour} \times 60 \text{ seconds/minute} \]
Calculating this gives:
\[ t = 24 \times 60 \times 60 = 86400 \text{ seconds} \]

### Step 4: Calculate the energy generated in one day.
Now, we can substitute the values of power and time into the energy formula:
\[ E = P \times t = (200 \times 10^6 \text{ W}) \times (86400 \text{ s}) \]

### Step 5: Perform the multiplication.
Calculating the energy:
\[ E = 200 \times 10^6 \times 86400 \]
\[ E = 17280000000 \text{ J} \]
This can also be expressed in scientific notation:
\[ E = 1.728 \times 10^{10} \text{ J} \]

### Final Answer:
The energy generated in a day by the atomic power station is:
\[ E = 1.728 \times 10^{10} \text{ J} \]