Question

The table illustrates the decay occurring in a 352-gram sample of vanadium-49 as time progresses.



Approximately how many grams of vanadium-49 will remain after a span of 1,320 days?

(1 point)
Responses

11
11

22
22

32
32

43

Answer 1

To determine how many grams of vanadium-49 will remain after 1,320 days, we need to know the half-life of vanadium-49. The half-life is the time it takes for half of the sample to decay.

Assuming that vanadium-49 has a half-life of around 330 days (this is a commonly accepted value), we can calculate the number of half-lives that fit into 1,320 days:

1. Calculate the number of half-lives in 1,320 days:
\[
\text{Number of half-lives} = \frac{1,320 \text{ days}}{330 \text{ days/half-life}} \approx 4
\]

2. Each half-life reduces the amount of vanadium-49 by half:
- After 1 half-life (330 days): \( \frac{352 \text{ g}}{2} = 176 \text{ g} \)
- After 2 half-lives (660 days): \( \frac{176 \text{ g}}{2} = 88 \text{ g} \)
- After 3 half-lives (990 days): \( \frac{88 \text{ g}}{2} = 44 \text{ g} \)
- After 4 half-lives (1,320 days): \( \frac{44 \text{ g}}{2} = 22 \text{ g} \)

So, approximately 22 grams of vanadium-49 will remain after 1,320 days.

The correct answer is **22**.