The main radioisotope in a banana is potassium-40, a beta emitter with an activity of 242 Bq/g. An average medium banana has about 320 mg of potassium and the natural abundance of potassium-40 is .0117%. Calculate the value of the BED in a.) Gy
b.) Sv
Assume 5.02 nGy/Bq
To calculate the BED (Biological Effective Dose) in Gy and Sv, we need to go through a series of steps. Here's how you can calculate it:
Step 1: Calculate the number of potassium-40 atoms in a medium banana.
To calculate the number of potassium-40 atoms, we need to know the natural abundance of potassium-40. The natural abundance of potassium-40 is given as 0.0117%.
Number of potassium-40 atoms = natural abundance of potassium-40 * total number of potassium atoms
Total number of potassium atoms = mass of potassium in the banana / molar mass of potassium
Given:
Natural abundance of potassium-40 = 0.0117% = 0.0117/100 = 0.000117
Total mass of potassium in a medium banana = 320 mg = 320 * 10^-3 g
Molar mass of potassium (K) = 39.10 g/mol
Calculations:
Total number of potassium atoms = (320 * 10^-3 g) / (39.10 g/mol)
Total number of potassium-40 atoms = 0.000117 * Total number of potassium atoms
Step 2: Calculate the total radioactivity of potassium-40 in the banana.
Radioactivity (Bq) = activity of potassium-40 * number of potassium-40 atoms
Given:
Activity of potassium-40 = 242 Bq/g
Number of potassium-40 atoms - calculated in Step 1
Calculations:
Total radioactivity of potassium-40 = (242 Bq/g) * Number of potassium-40 atoms
Step 3: Calculate the BED in Gy.
BED (in Gy) = Total radioactivity of potassium-40 * Conversion factor
Given: Conversion factor = 5.02 nGy/Bq
Calculations:
BED (in Gy) = (Total radioactivity of potassium-40) * (Conversion factor / 10^9)
Step 4: Calculate the BED in Sv.
BED (in Sv) = BED (in Gy) * quality factor
Given: quality factor = 1 (for beta particles)
Calculations:
BED (in Sv) = BED (in Gy) * 1
Now you can put all the given values and calculated values into the equations and solve for the BED in Gy and Sv.