Final answer:
It takes 7.646 days for 200 grams of radon-222 to decay to 50.0 grams by using its half-life of 3.823 days and applying the calculation for half-life decay.
Step-by-step explanation:
In order to determine how many days are required for 200 grams of radon-222 to decay to 50.0 grams, we need to calculate the number of half-lives that occur.
Radon-222 has a half-life of 3.823 days. Each half-life reduces the amount of radon-222 by half. So, if we divide 200 grams by 2 repeatedly until we reach 50 grams, we can determine the number of half-lives:
200 g / 2 = 100 g
100 g / 2 = 50 g
It took 2 half-lives to decay from 200 grams to 50 grams. Since each half-life is 3.823 days, we can multiply that by 2 to find the total number of days:
3.823 days/half-life × 2 half-lives = 7.646 days