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The force of interaction between two ato...

The force of interaction between two atoms is given by `F= alpha beta exp(-(x^2)/(alphakt))` , where x is the distance ,k is the Boltzmann constant and T is temperature and `alpha " and " beta` are two constans. The dimension of `beta` is :

A

`M^(2)L^2 T^(-2)`

B

`M^(0)L^2 T^(-4)`

C

`M^(2)LT^(-4)`

D

`MLT^(-2)`

Text Solution

Verified by Experts

The correct Answer is:
C
Exponential terms are dimensionless `(-(x^2)/(alpha kT)) = [M^(0)L^(0)T^(0)]`
`:. ([L^2])/([alpha][ML^2T^(-2)])=[M^(0)L^(0)T^(0)]` [kT is thermal energy]
`:. [alpha] = [M^(-1) T^(2)] " " :. [kT] = [ML^(2) T^(-2)]`
Now `[F] = [alpha beta]`
`:. [MLT^(-2)] =[M^(-1) T^(2) ][beta]`
`:. [beta] = [M^2 LT^(-4)]`
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