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The work done by a gas molecule in an isolated system is given by, W = α.β2.e-x2 / αkT, where x is the displacement, k is the Boltzmann constant and T is the temperature.α and β are constants. Then the dimensions of β will be

a. [M0LT0]

b. [M2LT2]

c. [MLT–2]

d. [ML2T–2]

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The correct option is c) MLT-2 

we knnow that ,x2 / α.k.T = dimensionless

[x2 / α.k.T ] = [M0L0T0]

[α] = [L2 / k.T]

⇒ [κ] = [M1L2T-2K-1]

[T] = [K]

⇒ [α] = [L2 / M1L2T-2K-1× K] ⇒ [α] = [M-1T2]

⇒ ω = α.β2

⇒ [M1L1T-2][L-1] / [M-1T2] = [β2] = [M2L2T-4]

[β] = [MLT-2]

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