OnlineCBT
Physics · UNITS AND MEASUREMENT
हिन्दीIn a physical calculation, pressure \( P \) varies with distance \( z \) according to the relation \( P = \frac{\alpha}{\beta} e^{-\frac{\alpha z}{k_B T}} \), where \( k_B \) is Boltzmann's constant and \( T \) is absolute temperature. The dimensional formula of \( \beta \) is:
Correct answer · Option 1
\( [\text{M}^0 \text{L}^2 \text{T}^0] \)
Explanation
The exponent of the exponential function is dimensionless, so \( [\frac{\alpha z}{k_B T}] = 1 \implies [\alpha] = \frac{[k_B T]}{[z]} = \frac{[M L^2 T^{-2}]}{[L]} = [M L T^{-2}] \). From \( [P] = [\frac{\alpha}{\beta}] \implies [\beta] = \frac{[\alpha]}{[P]} = \frac{[M L T^{-2}]}{[M L^{-1} T^{-2}]} = [M^0 L^2 T^0] \).
