RE-NEET 2026 Physics Blackbody Radiation MCQ Question

To find the dimensions of the expression $\sigma_s k_B^{-1} b$, we start with the known dimensions of each constant:

• The Stefan-Boltzmann constant $\sigma_s$ has dimensions $[M^1 L^{-2} T^{-3} K^{-4}]$.
• The Boltzmann constant $k_B$ has dimensions $[M^1 L^2 T^{-2} K^{-1}]$.
• The constant $b$ from Wien’s law has dimensions $[L]$.

Now, calculating $k_B^{-1}$:

$k_B^{-1} = [M^{-1} L^{-2} T^{2} K^{1}]$

Now, we combine the dimensions:

$\sigma_s k_B^{-1} b = [M^1 L^{-2} T^{-3} K^{-4}] \cdot [M^{-1} L^{-2} T^{2} K^{1}] \cdot [L]$

This simplifies to:

$[L^{-2} T^{-3} K^{-4} \cdot L^{-2} T^{2} K^{1} \cdot L] = [L^{-1} T^{-1} K^{-2}]$

Thus, the correct dimension is $[L^{-1} T^{-1} K^{-2}]$, which corresponds to option D. Other options fail because they either miscalculate the powers of $T$ or $K$.