The standard methods that apply to analytical chemistry still applies with radiochemical analytes. When the behavior of a radionuclide has to be taken into consideration such details are taken care of: The common methods available for separation are: $($i$)$ Complexation $($ii$)$ solvent $($iii$)$ Tracer adsorption.

Adsorption becomes very vital because the samples are recovered from radioactive matrix. Adsorption utilizes special equations called Langmuir adsorption isotherms which follows the equation.

$x=\frac{x_{m}b{C}_e}{1+b{C}_e},$ eqn $1.$

Where $x,=\frac{x}{m},$ the amount of solute adsorbed $x$ per unit mass of adsorbent $m.$

$Ce=$ Equilibrium constant of solute

$x_m=$ Amount of solute adsorbed per unit mass adsorbate required for mono layer of layer capacity.

b $,=$ a constant related to heat capacity of adsorption of material $=Q[bexp(-\frac{H}{R}T)]$

When the eqn $1$ is rearranged, it becomes:

$\frac{C_e}{x}=\frac{1}{b{x}_m}+\frac{C_e}{x_m},$ eqn $2.$

Which can further be rearranged as:

$\frac{1}{x}=\frac{1}{x_m}+\frac{1}{C_e}(\frac{1}{b{x}_m}),$ eqn $3$

Using equation $3,$ a linear plot of $\frac{1}{x}$ against $\frac{1}{C_e}$ is formed. The slope for this linear plot is $\frac{1}{b{x}_m}$ and $y$ intercept as $\frac{1}{x_m}$

The adsorption of one radioactive substance absorption behavior was evaluated and its data was as show below in table below.

$\backslash$table$[[\frac{s}{n},\backslash$table$[[$Mass of$],[$adsorbent$]],\backslash$table$[[$Volume of$],[$flask mL$]],\backslash$table$[[$Mass$],[$adsorbate$],[$adsorbed$]],\backslash$table$[[$Final COD$],[($mg$/$L$)$ C$]],\backslash$table$[[\frac{x}{m}$

The standard methods that apply to analytical chemistry still applies with radiochemical analytes. When the behavior of a radionuclide has to be taken into consideration such details are taken care of: The common methods available for separation are: $($i$)$ Complexation $($ii$)$ solvent $($iii$)$ Tracer adsorption.

Adsorption becomes very vital because the samples are recovered from radioactive matrix. Adsorption utilizes special equations called Langmuir adsorption isotherms which follows the equation.

$x=\frac{x_{m}b{C}_e}{1+b{C}_e},$ eqn $1.$

Where $x,=\frac{x}{m},$ the amount of solute adsorbed $x$ per unit mass of adsorbent $m.$

$Ce,=$ Equilibrium constant of solute

$x_m=$ Amount of solute adsorbed per unit mass adsorbate required for mono layer of layer capacity.

b $,=$ a constant related to heat capacity of adsorption of material $=Q[bexp(-\frac{H}{R}T)]$

When the eqn $1$ is rearranged, it becomes:

$\frac{C_e}{x}=\frac{1}{b{x}_m}+\frac{C_e}{x_m},$ eqn $2.$

Which can further be rearranged as:

$\frac{1}{x}=\frac{1}{x_m}+\frac{1}{C_e}(\frac{1}{b{x}_m}),$ eqn $3$

Using equation $3,$ a linear plot of $\frac{1}{x}$ against $\frac{1}{C_e}$ is formed. The slope for this linear plot is $\frac{1}{b{x}_m}$ and $y$ intercept as $\frac{1}{x_m}$

The adsorption of one radioactive substance absorption behavior was evaluated and its data was as show below in table below.

See the attached scan for the whole question.