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  4. The Richardson equation is given by I = AT2 e-B/kT. The dimensional formula for AB2 is same as that for

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Q. The Richardson equation is given by $I = AT^2\, e^{-B/kT}$. The dimensional formula for $AB^2$ is same as that for

Physical World, Units and Measurements

Solution:

$I=AT^{2}\,e^{-B/kT}$
Dimensionally, $A = I/T^2$, dimensions of $B = kT$
($\because$ power of exponential is a number)
$AB^{2}=\frac{I}{T^{2}}\left(kT\right)^{2}=Ik^{2}$