Question

Your job is to determine the concentration of leucine in a 5.0 mL solution containing 14C-leucine. You remove 5.0 L of the solution for counting and obtain 6.2 x 105 CPM. Assume the counting efficiency is 40.0%. The specific radioactivity of the 14C-leucine is 0.600 mCi/mgram. Calculate the concentration of leucine in mmolar units.

Answer 1

The given data is

The specific radioactivity of the 14C-leucine = 0.6 mCi/mg

Counting efficiency =40 %

The counts obtained for  5.0 L of the solution (please note that there is a printing mistake, hence I consider 5.0 L as 5 mL) = 6.2 x10⁵ CPM

Counting efficiency = Number of Photons counted by detector/Number of Photons emitted by the radiation source

From above equation, the number of disintegrations per minute (dpm) can be = 6.2 x10⁵ /0.4 =

6.2 x2.5x10⁵ dpm = 6.2 x2.5x10⁵x60 dps= 9.3x10⁷ dps (Note dps = disintegrations per second)

So the 14C-leucine present in 5 ml gives the 9.3x10⁷ disintegrations per second ........(I)

The specific radioactivity can be defined as activity per quantity of a radio nuclide.

From the data, specific radioactivity = 0.6 mCi/mg

We know that one curie (Ci) = 3.7x10¹⁰ disintegrations per second (dps)

So above specific radioactivity can be converted into disintegrations per second (dps)as follows

specific radioactivity = 0.6 x10^-3x3.7x10¹⁰ = 2.22x10⁷ dps/mg

Means one mg of 14C-leucine gives 2.22x10⁷ disintegrations per second .......(II)

From (I) and (II), the weight of 14C-leucine present in 5 mL solution =  9.3x10⁷ /2.22x10⁷ = 4.189 mg.

Hence the concentration of leucine = 4.189 mg/5 mL = 0.8378 g/L

Molecular weight of leucine = 131.175 g/mol

So the concentration of leucine = 0.006386 mol/L = 6.386 mmol/L = 6.386 mM

The concentration of leucine is 6.386 in mmolar units