The force of interaction between two atoms is given by F = αβ exp where x is the distance, k is the Boltzmann constant and T is temperature and α and β are two constants. The dimension of β is:

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Physics

Dimensions

Question

The force of interaction between two atoms is given by F = αβ exp $(- \frac{x^{2}}{αkt})$ where x is the distance, k is the Boltzmann constant and T is temperature and α and β are two constants. The dimension of β is:

M²LT^-4

MLT^-2

M²L²T^-2

M⁰L²T^-4

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Power of e should be dimensionless.

So, [λ] = (αTk)

⇒ L² = [α] (ML² T²)

⇒ (α) = (M^–1 T²)

⇒ $E = \frac{1}{2} KT$

⇒ (ML²T^–2 ) ; (E) = [KT)

⇒ (αβ) = (F)

⇒ (M^–1 T²) (β) = (MLT^–2)