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The time dependence of a physical quantity $P$ is given by $P=P_{0} e_{\alpha}\left(-\alpha t^{2}\right)$, where $\alpha$ is a constant and $t$ is time. The constant $\alpha$
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has dimensions of $T^{-2}$
Given, $\mathrm{P}=\mathrm{P}_{0} \exp \left(-\alpha \mathrm{t}^{2}\right)$
As $\mathrm{P}$ and $\mathrm{P}_{0}$ have the same units, therefore $\alpha t^{2}$ must be dimensionless for which
$\alpha=\frac{1}{T^{2}}=T^{-2}$
As $\mathrm{P}$ and $\mathrm{P}_{0}$ have the same units, therefore $\alpha t^{2}$ must be dimensionless for which
$\alpha=\frac{1}{T^{2}}=T^{-2}$
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