Question

Define the followings.
(a) collision flux
(b) Stokes law
(c) Fick's second law
(d) Einstein-Smoluchowski equation
(e) half-life of a first-order reaction
(f) Forster theory of resonance energy transfer
(g) Mechaelis-Menten mechanism

Answer 1

a) Collision flux ;- The collision flux is defined as the number of collisions per unit area (A) and unit time (t) . And it is given as

Collision flux = Z_w = N * ( k *T / 2 * pi * m )^1/2

where N = number densiy of molecules .

k = Boltzmanns constant

b) Stokes law ;- The frictional force or the drag force exerted on a spherical particles with a small reynolds number in a viscous medium is known as the stokes law and it is given as

F_d = 6 * pi * n * R * V

where F_d is the frictional force – known as Stokes' drag – acting on the interface between the fluid and the particle.

n = dynamic viscosity

R is the radius of the spherical object

V is the flow velocity relative to the object.

c) Ficks second law ;- Ficks second law predicts how diffusion causes concentration to change with time . And it is given as

  dC / dt = D *( d²C / dx² )

where C = concentration of the diffusing species

t = time

D = diffusion coefficient

x = position or length

d) Einstein - Smoluchowski equation ;- It is given as

D = μ * k_B * T

where

D is the diffusion constant;

μ is the "mobility", or the ratio of the particle's terminal drift velocity to an applied force, μ = v_d / F;

k_B is Boltzmann's constant;

T is the absolute temperature.

e) Half life of a first order reaction ;- For a first order reaction like A ------.> products

the rate is given as rate = k [A] where k is the rate constant and [A] is the concentration of the reacting species.

for a first order reaction the half life is independent of concentration .

half life or t_1/2   = 0.693 / k.

f) Forster theory of resonance energy transfer ;- It is the mechanism describing energy transfer between two light-sensitive molecules or chromophores.

g) Mechaelis - menten equation ;- Michaelis-Menten equation is the equation describing the rate of enzymatic reactions by relating the reaction rate (v) to the [S] which is the concentration of a substrate (S).

And the equation is given by v = V_max * [S] / (K_M + [S])

where V_max is the maximum rate achieved by the system at the saturating substrate concentration.

K_M is the Michaelis constant which is the substrate concentration at which the reaction rate is half of Vmax.

Certain Bio-chemical reactions involving a single substrate are often assumed to follow the Michaelis-Menten equation.