Unit of Stefan's constant is

The correct option is Jm⁻²s⁻¹K⁻⁴.

Step-by-step derivation:

According to the Stefan-Boltzmann law, the total radiant energy emitted per unit area per second (emissive power, $E$) of a black body is directly proportional to the fourth power of its absolute temperature ($T$).
This relationship is mathematically expressed as:

$E=\sigma T^4$

where $\sigma$ is Stefan's constant.

We can rearrange this formula to solve for Stefan's constant ($\sigma$):

$\sigma =\frac{E}{T^4}$

Since emissive power ($E$) is defined as the energy radiated per unit area per unit time, we can write:

$E=\frac{\text{Energy}}{\text{Area}\times \text{Time}}$

Substituting this back into the expression for $\sigma$, we get:

$\sigma =\frac{\text{Energy}}{\text{Area}\times \text{Time}\times {\text{Temperature}}^4}$

Now, let's substitute the standard units for each of the quantities involved:
- Energy is measured in Joules (J)
- Area is measured in square meters (m²)
- Time is measured in seconds (s)
- Temperature is measured in Kelvin (K)

Substituting these units gives:

$\text{Unit of}\sigma =\frac{\text{J}}{{\text{m}}^2·\text{s}·{\text{K}}^4}={\text{Jm}}^{-2}{\text{s}}^{-1}{\text{K}}^{-4}$

Therefore, the unit of Stefan's constant is Jm⁻²s⁻¹K⁻⁴.