Protein x has an absorptivity of 0.4 ml·mg-1 ·cm-1 at 280 nm. what is the absorbance at 280 nm of a 2.0 mg ·ml-1 solution of protein x? (assume the light path is 1cm).

Absorbance measures the ability of the substance to absorb light at a specific wavelength.

Absorbance is also equal to the product of molar absorptivity, path length and molar concentration.

The mathematical expression is given as:

      (1)

where, A = absorbance

=  molar absorptivity

l = path length

c  = molar concentration.

The above formula is said to Beer's Law.

Absorptivity of protein x  =

Path length = 1 cm

Molar concentration =

Put the values in formula (1)

=

Thus, absorbance at 280 nm =

part 1: the half-life of the element is 22 years.

part 2: it will take 132.02 year for the sample to decay from 308.0 g to 4.8125 g.

explanation:

part 1: there are two ways to determine the half life time.

first way: the half life time can be determined directly from its definition as it is the time required for the sample to decay to its half concentration.

from the data the initial concentration was 45.0 g and decayed to its half value (22.5 g) in 22.0 years.

second way: the radio active decay is considered first order reaction so we can use the laws of first order reactions.

k = (1/t) ln (a/a-x), where k is the rate constant of the reaction,

t is the time of the reaction

a is the initial concentration of the reactant

a-x is the remaining concentration at time (t)

a = 45.0 g the initial concentration at t = 0 year.

at t = 22 year, a-x = 22.5 g

then k = (1/22 year) ln (45.0 g/ 22.5 g) = 0.0315 year-1.

the half-life time (t1/2) = ln 2/ k = 0.693/ k =0.693/ 0.0315 = 22 years.

part 2:

using the same law k = (1/t) ln (a/a-x),

using the given data; a = 308.0 g and a-x = 4.8125 g and the calculated k from the part 1 (k = 0.0315 year-1)

t = (1/k) ln (a/a-x) = (1/0.0315) ln (308.0/ 4.8125) = 132.02 years

hey your not cool]