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Dimensional Analysis

The Richardso...

Question

The Richardson equation is given by $I = A T^{2} e^{- B / k T}$ . The dimensional formula for $A B^{2}$ is same as that for

I T^{2}

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k T

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I k^{2}

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I k^{2} / T

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Solution

The correct option is B $I k^{2}$
$I = A T^{2} e^{- B / k T}$
Dimensionally, $A = I / T^{2}$ , dimensions of B = kT
( $∵$ power of exponential is a number)
$A B^{2} = \frac{I}{T^{2}} (k T)^{2} = I k^{2}$

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