Final answer:
After using the formula for radioactive decay, we find that approximately 192.65g remains of the radioactive element after 1 week.
Step-by-step explanation:
To solve this problem, we can use the formula for radioactive decay: A = A0 * (1/2)(t / T1/2), where A is the final amount, A0 is the initial amount, t is the time elapsed, and T1/2 is the half-life.
Step-by-step solution:
- Initial amount, A0 = 300g
- Final amount, A = 220g
- Time elapsed, t = 48 hours
- Half-life, T1/2 = unknown
- Using the formula A = A0 * (1/2)(t / T1/2), we can write the equation:
220 = 300 * (1/2)(48 / T1/2)
- Solving for T1/2 gives us T1/2 = 48 * ln(2) / ln(300/220)
Substituting the value of T1/2 into the equation gives us:
A = 300 * (1/2)(t / (48 * ln(2) / ln(300/220)))
- Calculating the amount after 1 week (7 days) by substituting t = 7 * 24 hours into the equation gives us :
A = 300 * (1/2)(7 * 24) / (48 * ln(2) / ln(300/220)))
- Calculating the final value of A gives us A = 192.65g
Therefore, after 1 week, approximately 192.65g remains of the radioactive element.