F=α (β e)(- (x/α k t)) k= Boltzmann constant t= temperature x= distance The dimensions of β is

Question

F=α (β e)(- (x/α k t)) k= Boltzmann constant t= temperature x= distance The dimensions of β is (A) [M L T- 4] (B) [M- 2 L- 2 T4] (C) [M L T- 2] (D) [M2 L T- 1]

Tardigrade Admin · Accepted Answer

F=α (β e)(- (x/α K T)) (x/α )=[ML2 T- 2] α =[M- 1 L- 1 T- 2] [MLT- 2]=[M- 1 L- 1 T2][β ]- 1 β =[M- 2 L- 2 T4]

Q. $F = α (β e)^{(- \frac{x}{α k t})}$

$k =$ Boltzmann constant

$t =$ temperature

$x =$ distance

The dimensions of $β$ is

$[M L T^{- 4}]$

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

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

$[M^{2} L T^{- 1}]$

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

Q. F=α(βe)(−αktx​) k= Boltzmann constant t= temperature x= distance The dimensions of β is

[MLT−4]

[M−2L−2T4]

[MLT−2]

[M2LT−1]