The temperature of a body is increased by `50%`. The amount of radiation emitted by it would be nearly

Options

A. `50 %`
B. `225 %`
C. `250 %`
D. `400 %`

Explanation

To solve the problem of how the amount of radiation emitted by a body changes when its temperature is increased by 50%, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Initial Temperature**:
Let the initial temperature of the body be \( T \).

2. **Calculate the New Temperature**:
If the temperature is increased by 50%, the new temperature \( T' \) can be calculated as:
\[ T' = T + 0.5T = 1.5T \]

3. **Use the Stefan-Boltzmann Law**:
According to the Stefan-Boltzmann law, the amount of radiation emitted \( E \) by a body is proportional to the fourth power of its absolute temperature:
\[ E \propto T^4 \]
Therefore, the initial radiation emitted \( E \) at temperature \( T \) is:
\[ E = kT^4 \]
where \( k \) is a constant.

4. **Calculate the Radiation at the New Temperature**:
The radiation emitted at the new temperature \( T' \) is:
\[ E' = k(T')^4 = k(1.5T)^4 = k \cdot (1.5^4) \cdot T^4 \]

5. **Calculate \( 1.5^4 \)**:
We need to calculate \( 1.5^4 \):
\[ 1.5^4 = (1.5 \times 1.5) \times (1.5 \times 1.5) = 2.25 \times 2.25 = 5.0625 \]

6. **Express the New Radiation in Terms of the Old Radiation**:
Now we can express \( E' \) in terms of \( E \):
\[ E' = 5.0625 \cdot E \]

7. **Calculate the Increase in Radiation**:
The increase in radiation can be calculated as:
\[ \text{Increase} = E' - E = 5.0625E - E = 4.0625E \]

8. **Calculate the Percentage Increase**:
To find the percentage increase in radiation:
\[ \text{Percentage Increase} = \left( \frac{E' - E}{E} \right) \times 100 = \left( \frac{4.0625E}{E} \right) \times 100 = 406.25\% \]

### Final Answer:
The amount of radiation emitted by the body would increase by approximately **406.25%**.