Q 11-01-004NEETNEET 2026Top questionMedium
Consider that $\sigma_s$, $k_B$, $b$ represent Stefan-Boltzmann constant, Boltzmann constant and Wien's displacement law constant, respectively. The dimension of $\sigma_s k_B^{-1} b$ is :
Answer: (A) $[\mathrm{L^{-1}T^{-1}K^{-2}}]$
Stefan-Boltzmann constant ($E = \sigma T^4$, energy per unit area per unit time):
$$[\sigma_s] = \frac{[\mathrm{ML^2T^{-2}}]}{[\mathrm{L^2}][\mathrm{T}][\mathrm{K^4}]} = [\mathrm{MT^{-3}K^{-4}}]$$
Boltzmann constant (energy per kelvin): $[k_B] = [\mathrm{ML^2T^{-2}K^{-1}}]$
Wien's constant ($\lambda_m T = b$): $[b] = [\mathrm{LK}]$
$$[\sigma_s k_B^{-1} b] = \frac{[\mathrm{MT^{-3}K^{-4}}][\mathrm{LK}]}{[\mathrm{ML^2T^{-2}K^{-1}}]} = [\mathrm{L^{-1}T^{-1}K^{-2}}]$$
Solution by Sreeraj P, M.Sc Physics