The force of interaction between two atoms is given by ; where is the distance, is the Boltzmann constant and T is temperature and and are two constants. The dimensions of is:

Question

The force of interaction between two atoms is given by $F = α β \exp (- \frac{x^{2}}{α k T})$ ; where $' x'$ is the distance, $' k'$ is the Boltzmann constant and T is temperature and $α$ and $β$ are two constants. The dimensions of $β$ is:

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(2)

Force of interaction between two atoms, $F = α β e^{(\frac{- x^{2}}{α k T})}$

Since exponential terms are dimensionless

$∴$ $α β e^{(\frac{- x^{2}}{α k T})}$

$[F] = [α] [β]$

$M L T^{- 2} = M^{- 1} T^{2} [β]$

$\Rightarrow$ $[β] = M^{2} L T^{- 4}$

Solution

Q.
The force of interaction between two atoms is given by $F = α β \exp (- \frac{x^{2}}{α k T})$ ; where $' x'$ is the distance, $' k'$ is the Boltzmann constant and T is temperature and $α$ and $β$ are two constants. The dimensions of $β$ is:

1 $M^{0} L^{2} T^{- 4}$

2 $M^{2} {LT}^{- 4}$

3 ${MLT}^{- 2}$

4 $M^{2} L^{2} T^{- 2}$

Ans.
(2)

Force of interaction between two atoms, $F = α β e^{(\frac{- x^{2}}{α k T})}$

Since exponential terms are dimensionless

$∴$ $α β e^{(\frac{- x^{2}}{α k T})}$

$[F] = [α] [β]$

$M L T^{- 2} = M^{- 1} T^{2} [β]$

$\Rightarrow$ $[β] = M^{2} L T^{- 4}$

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Solution

Q. The force of interaction between two atoms is given by F=αβexp(-x2αkT); where 'x' is the distance, 'k' is the Boltzmann constant and T is temperature and α and β are two constants. The dimensions of β is:

1 M0L2T-4

2 M2LT-4

3 MLT-2

4 M2L2T-2

Ans. (2) Force of interaction between two atoms, F=αβe(-x2αkT) Since exponential terms are dimensionless ∴ αβe(-x2αkT) [F]=[α][β] MLT-2=M-1T2[β] ⇒ [β]=M2LT-4