Radiation energy corresponding to the temperature T of the sun is E. If its temperature is doubled, then its radiation energy will be :

Options

A. 32 E
B. 16 E
C. 8 E
D. 4 E

Explanation

To solve the problem, we need to understand how radiation energy relates to temperature. According to the Stefan-Boltzmann law, the radiation energy emitted by a black body is proportional to the fourth power of its absolute temperature (T).

### Step-by-Step Solution:

1. **Understand the relationship**: The radiation energy (E) is proportional to the fourth power of the temperature (T). Mathematically, this can be expressed as:
\[ E \propto T^4 \]
This means if we have a temperature T, the radiation energy is given by:
\[ E = k \cdot T^4 \]
where k is a constant of proportionality.

2. **Initial conditions**: We know that at temperature T, the radiation energy is:
\[ E = k \cdot T^4 \]

3. **Doubling the temperature**: If the temperature is doubled, the new temperature becomes:
\[ T' = 2T \]

4. **Calculate the new radiation energy**: The new radiation energy (E') at temperature T' can be expressed as:
\[ E' = k \cdot (T')^4 = k \cdot (2T)^4 \]

5. **Simplifying the expression**: Expanding the equation:
\[ E' = k \cdot (2^4 \cdot T^4) = k \cdot 16 \cdot T^4 \]
Since we know that \( E = k \cdot T^4 \), we can substitute this into the equation:
\[ E' = 16 \cdot (k \cdot T^4) = 16E \]

6. **Final answer**: Therefore, the new radiation energy when the temperature is doubled is:
\[ E' = 16E \]

### Conclusion:
The radiation energy corresponding to the doubled temperature of the sun will be \( 16E \).