To determine how many grams of vanadium-49 will remain after 1,320 days, we need the half-life of vanadium-49. Vanadium-49 has a half-life of approximately 330 days. This means that every 330 days, half of the remaining vanadium-49 will decay.
-
Calculate the number of half-lives in 1,320 days: \[ \text{Number of half-lives} = \frac{1320 \text{ days}}{330 \text{ days/half-life}} = 4 \]
-
Start with the initial amount of vanadium-49: \[ \text{Initial amount} = 352 \text{ grams} \]
-
After each half-life, the remaining amount is halved. Therefore, after 4 half-lives:
- After 1st half-life: \( 352 \div 2 = 176 \) grams
- After 2nd half-life: \( 176 \div 2 = 88 \) grams
- After 3rd half-life: \( 88 \div 2 = 44 \) grams
- After 4th half-life: \( 44 \div 2 = 22 \) grams
Thus, after 1,320 days, approximately 22 grams of vanadium-49 will remain.
The correct response is: 22