Final answer:
To find the activity of 5 freshly picked bananas, multiply the activity of one banana by 5. An average banana contains 0.000468 grams of potassium-40. The activity of 0.000468 grams of potassium-40 is 122.8792 Bq, so the activity of 5 bananas is 614.396 Bq.
Step-by-step explanation:
To find the activity of 5 freshly picked bananas, we need to calculate the activity of one banana and then multiply it by 5. First, we need to find the mass of radioactive potassium-40 (40K) in one banana. We can use the given information that an average banana contains 0.39 grams of potassium and 0.012% of that is potassium-40. Therefore, the mass of potassium-40 in one banana is 0.39 grams * 0.012% = 0.000468 grams.
Next, we can use the activity of 1 gram of potassium-40 (2.626 × 105 Bq) to find the activity of 0.000468 grams.
The activity of 0.000468 grams of potassium-40 is calculated as follows:
Activity = (0.000468 grams / 1 gram) * (2.626 × 105 Bq) = 122.8792 Bq
Therefore, the activity of 5 freshly picked bananas is 5 * 122.8792 Bq = 614.396 Bq.