Given, work done by gas molecule, W=α2βe−βx2∕kT Here, x is displacement, k is Boltzmann constant, α and β are constants and T is temperature. Dimensional formula of [W]=[ML2T−2] ∴ Dimensions of [α2β]=[ML2T−2] ⇒α=[
ML2T−2
β
]1∕2 . . . (i) The term [e−βx2∕kT] should be dimensionless, i.e. [M0L0T0]. ⇒[
βx2
kT
]=[M0L0T0] ⇒[β]=
[k][T]
[x2]
. . . (ii) Energy of gaseous molecule (E)=
7
2
kT [k]=[E]∕[T]=[ML2T−2K−1] Substituting the value of k in Eq. (ii), we get [β]=
[ML2T−2K−1][K]
[L2]
=[MT−2] Substituting the value of β in Eq. (i), we get [α]={