Determine the fraction of an original sample of rn-222 that remains unchanged after 7.646 days

Radon-222 or Rn-222 has a half-life of 3.82 days. To determine the fraction of an original sample of Rn-222 that remains unchanged after 7.646 days, we calculate the amount of Rn-222 remaining after 7.646 days and divide it with the original amount. Using 1 gram as a basis and using half-life calculation methods, we can determine that 0.249 or 0.25 grams of Rn-222 will remain, and thus the fraction remaining is 0.25 or 1/4.