Question : The number of particles crossing a unit area perpendicular to x axis in a unit time n is given by n=-D(n2-n1/x2-x1) where n1, n2 are number of particles per unit volume for the value of x meant to be x1 and x2 respectively. Find the dimensions of the diffusion constant D.
Doubt bt Riddhi
Solution :
n=-D(n2-n1/x2-x1)
D=-n(x2-x1/n2-n1)
Here
n = No. of particles crossing unit area per unit time
n = Numbers / (Area × Time)
n = Numbers / (Area × Time)
Dimensional formula of n = [L-2T-1]
n1, n2 = No. of particles per unit volume
= Number / Volume
Dimensional formula of n1 or n2 = [L-3]
Dimensional formula of n1 or n2 = [L-3]
x1, x2 = Distance
Dimensional formula of x1 or x2 = [L]
D=-n(x2-x1/n2-n1)
Dimensional Formula of D
= [L-2T-1][L]/[L-2T-1]
= [L-1T-1]/[L-3]
= [L-2T-1][L]/[L-2T-1]
= [L-1T-1]/[L-3]
= [L2T-1]
Hence, the dimensional formula of Diffusion constant (D) is [M0L2T-1]