2026 Re-NEET Units and MeasurementsDimensional analysis Medium Question 4 of 53 in Units and Measurements

Consider that $\sigma_s$, $k_B$, b represents Stefan-Boltzmann constant, Boltzmann constant and Wien's displacement law constant, respectively. The dimension of $\sigma_sk_B^{-1}b$ is

A $[L^{-1}T^{-1}K^{-2}]$
B $[L^{-1}K^{-2}]$
C $[L^{-1}T^{-1}K^{-3}]$
D $[L^{-1}T^{-1}K^{-4}]$

The answer is A.

Solution

$[\sigma_s][k_B^{-1}][b]=\left[\frac{Intensity}{(Temp)^4}\right]\left[\frac{Energy}{Temp}\right]^{-1}[\lambda_{max}\,Temp]=\left[\frac{MT^{-3}}{K^4}\right]\left[\frac{ML^2T^{-2}}{K}\right]^{-1}[LK]=[M^0L^{-1}T^{-1}K^{-2}]$.

Concept Dimensional analysis

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