Distribution of energy in the spectrum of a black body can be correctly represented by .

Options

A. Stefan's law
B. Kirchoff's law
C. Planks's law
D. Wien's law

Explanation

To solve the question regarding the distribution of energy in the spectrum of a black body, we need to analyze the different laws related to black body radiation.

### Step-by-Step Solution:

1. **Understanding Black Body Radiation**: A black body is an idealized physical object that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence. The energy emitted by a black body is a function of its temperature and the wavelength of the radiation.

2. **Reviewing the Relevant Laws**:
- **Stefan-Boltzmann Law**: This law states that the total energy emitted per unit surface area of a black body is proportional to the fourth power of its absolute temperature (T). The formula is given by:
\[ E = \sigma T^4 \]
where \(E\) is the total energy emitted, \(\sigma\) is the Stefan-Boltzmann constant, and \(T\) is the absolute temperature. However, this law does not provide the distribution of energy across different wavelengths.

- **Kirchhoff's Law**: This law relates the emissive power of a body to its absorptive power at thermal equilibrium. It states that the emissive power of a body is equal to the absorptive power of a black body at the same temperature. This law does not describe the spectral distribution of energy.

- **Planck's Law**: This law provides a formula for the spectral distribution of energy emitted by a black body at a given temperature. It states that the energy emitted per unit wavelength is given by:
\[ E(\lambda, T) = \frac{2hc^2}{\lambda^5} \cdot \frac{1}{e^{\frac{hc}{\lambda kT}} - 1} \]
where \(E(\lambda, T)\) is the energy emitted at wavelength \(\lambda\), \(h\) is Planck's constant, \(c\) is the speed of light, \(k\) is Boltzmann's constant, and \(T\) is the absolute temperature. This law accurately describes the distribution of energy across different wavelengths.

- **Wien's Displacement Law**: This law states that the wavelength at which the emission of a black body spectrum is maximized is inversely proportional to the temperature. It is given by:
\[ \lambda_{max} \cdot T = b \]
where \(b\) is Wien's displacement constant. This law is also limited to the maximum wavelength and does not provide a complete spectral distribution.

3. **Conclusion**: Among the laws discussed, **Planck's Law** is the only one that correctly represents the distribution of energy in the spectrum of a black body across all wavelengths. Therefore, the correct answer to the question is **Planck's Law**.

### Final Answer:
The distribution of energy in the spectrum of a black body can be correctly represented by **Planck's Law**.