sodium-24 has a half-life of 15 hours how much of a 20 gram sample would remain after 30 hours? and how do you solve this?

Ah, the curious case of sodium-24! Well, here's how you can tackle this radioactive riddle.

After 15 hours, half of the sodium-24 will decay, leaving you with 10 grams. Now, for the next 15 hours, we'll have to witness yet another half-life performance. So, after 30 hours, we'll have another "POOF!" and *ta-da* half of the remaining sodium-24 is gone.

To calculate this, let's break it down step by step:

30 hours / 15 hours = 2 half-lives

Since each half-life reduces the amount by half, we'll multiply the initial amount (20 grams) by (1/2) for each half-life.

20 grams x (1/2) x (1/2) = 5 grams

So, after 30 hours, approximately 5 grams of sodium-24 will be left from the initial 20-gram sample. Just like that, the sodium-24 vanishes into thin air, leaving behind a lighter but perhaps still salty residue.

To solve this problem, we can use the half-life formula:

Amount remaining = Initial amount × (0.5)^(time / half-life)

Given that the half-life of sodium-24 is 15 hours, we can substitute the values into the formula:

Amount remaining = 20 grams × (0.5)^(30 hours / 15 hours)

Let's compute the amount remaining step by step:

1. Calculate the exponent:

30 hours / 15 hours = 2

2. Raise 0.5 to the power of 2:

(0.5)^2 = 0.25

3. Multiply the initial amount by the result:

Amount remaining = 20 grams × 0.25

4. Calculate the final result:

Amount remaining = 5 grams

Therefore, after 30 hours, only 5 grams of the initial 20-gram sample of sodium-24 would remain.

To find out how much of a 20-gram sample of sodium-24 would remain after 30 hours, we can use the concept of half-life. The half-life of sodium-24 is given as 15 hours, which means that after every 15 hours, the amount of sodium-24 present is reduced by half.

To solve this, we can follow these steps:

1. Determine the number of half-life periods that have passed. In this case, we have 30 hours and a half-life of 15 hours. Since 30 divided by 15 equals 2, we know that two half-life periods have passed.

2. Calculate the remaining amount of sodium-24 after each half-life period. After the first half-life (15 hours), half of the sample would remain, so the amount would be 20 grams divided by 2, which is 10 grams. After the second half-life (another 15 hours), half of the remaining sample (10 grams) would remain, resulting in 10 grams divided by 2, which is 5 grams.

Therefore, after 30 hours, 5 grams of sodium-24 would remain from the initial 20-gram sample.

30 hr is two half-lives ... 30 / 15 = 2

each half-life reduces the amount by half

20 g * 1/2 * 1/2 = ?