The energy reveived from the sun by the earth and surrounding atmosphere is 2 cal `cm^(-2)` "min"`^(-1)` on a surface normal to the rays of sun.
Q. What is the total energy received, in joule, by the earth and its atmosphere?

Options

A. `10.645xx10^(18)J"min"^(-1)`
B. `10.645xx10^(15)J"min"^(-1)`
C. `8.645xx10^(17)J"min"^(-1)`
D. `9.645xx10^(14)J"min"^(-1)`

Explanation

To solve the problem of finding the total energy received by the Earth and its atmosphere from the sun, we can follow these steps:

### Step 1: Understand the given data
The energy received from the sun is given as \(2 \, \text{cal} \, \text{cm}^{-2} \, \text{min}^{-1}\). We need to convert this energy into joules and then calculate the total energy received by the Earth.

### Step 2: Convert the energy from calories to joules
1 calorie is equivalent to approximately 4.2 joules. Therefore, we can convert the energy received:
\[ \text{Energy in joules} = 2 \, \text{cal} \times 4.2 \, \text{J/cal} = 8.4 \, \text{J/cm}^2 \, \text{min}^{-1} \]

### Step 3: Calculate the surface area of the Earth
The radius of the Earth is given as \(6400 \, \text{km}\). First, convert this to meters:
\[ R = 6400 \, \text{km} = 6400 \times 10^3 \, \text{m} = 6.4 \times 10^6 \, \text{m} \]
The surface area \(A\) of a sphere is given by the formula:
\[ A = 4\pi R^2 \]
Substituting the radius:
\[ A = 4\pi (6.4 \times 10^6)^2 \]

### Step 4: Calculate the area in square meters
Calculating \(R^2\):
\[ (6.4 \times 10^6)^2 = 40.96 \times 10^{12} \, \text{m}^2 \]
Now substituting into the area formula:
\[ A = 4\pi (40.96 \times 10^{12}) \approx 513.126 \times 10^{12} \, \text{m}^2 \]

### Step 5: Convert area from square meters to square centimeters
Since \(1 \, \text{m}^2 = 10^4 \, \text{cm}^2\):
\[ A \approx 513.126 \times 10^{12} \times 10^4 \, \text{cm}^2 = 5.13126 \times 10^{16} \, \text{cm}^2 \]

### Step 6: Calculate the total energy received by the Earth
Now, we can calculate the total energy received in joules per minute:
\[ \text{Total Energy} = \text{Energy per unit area} \times \text{Area} \]
Substituting the values:
\[ \text{Total Energy} = 8.4 \, \text{J/cm}^2 \, \text{min}^{-1} \times 5.13126 \times 10^{16} \, \text{cm}^2 \]
Calculating this gives:
\[ \text{Total Energy} \approx 4.303 \times 10^{17} \, \text{J/min} \]

### Step 7: Final conversion to joules
Since the question asks for the total energy received in joules, we can state:
\[ \text{Total Energy} \approx 4.303 \times 10^{17} \, \text{J/min} \]

### Conclusion
The total energy received by the Earth and its atmosphere from the sun is approximately \(4.303 \times 10^{17} \, \text{J/min}\).

---