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Question:

The force of interaction between two atoms is given by F = αβ exp(−x²α/kT); 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⁻¹

MLT⁻¹

M²L²T⁻¹

M⁰L²T⁻¹

Solution:

The correct option is B M²LT⁻¹
F = αβe^(−x²α/kT)
[x²α/kT] = M⁰L⁰T⁰
L²[α]/(ML²T⁻¹)=M⁰L⁰T⁰
[α] = M¹T²
[F] = [α][β] = MLT⁻¹
M¹T²[β] = MLT⁻¹
→[β] = M²LT⁻¹