Question

The time dependence of physical quantity $P$ is found to be of the form $P=P_o{e}^{-\alpha t^2}$, where $‘t^{\prime }$ is the time and $\alpha$ is some constant. Then the constant $\alpha$ will

• A. be dimensionless
• B. have dimensions of $T^{-2}$
• C. have dimensions of $P$
• D. have dimensions of $P$ multiplied by $T^{-2}$

Answer 1

The correct option is B have dimensions of $T^{-2}$

From the given expression:
$P=P_o{e}^{-\alpha t^2}$

Here, the exponent of $e$, cannot have any dimensions.
$\therefore \left[\alpha \right]=[t^2{]}^{-1}$
$\left[\alpha \right]=\left[T^{-2}\right]$