The force of interaction between two atoms is given by F = α β exp ( - (x2/α 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 :

Question

The force of interaction between two atoms is given by F = α β exp ( - (x2/α 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 : (A) M2 L2 T-2 (B) M2 L T-4 (C) M0 L2 T-4 (D) MLT-2

Tardigrade Admin · Accepted Answer

F =αβ e((-x2/α KT)) [(x2/α KT)] =M°L°T° (L2/[α]ML2 T-2) =M°L°T° ⇒ [α] =M-1 T2 [F] =[α][β] MLT-2 =M-1T2[β] ⇒ [β] =M2LT-4

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

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

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

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

$M L T^{- 2}$

$F = α β e^{(\frac{- x ^{2}}{α K T})}$
$[\frac{x ^{2}}{α K T}] = M^{\circ} L^{\circ} T^{\circ}$
$\frac{L ^{2}}{[ α ] M L ^{2} T ^{- 2}} = M^{\circ} L^{\circ} T^{\circ}$
$\Rightarrow [α] = M^{- 1} T^{2}$
$[F] = [α] [β]$
$M L T^{- 2} = M^{- 1} T^{2} [β]$
$\Rightarrow [β] = M^{2} L T^{- 4}$

Q. The force of interaction between two atoms is given by F=αβexp(−αktx2​); 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 :

M2L2T−2

M2LT−4

M0L2T−4

MLT−2