Final answer:
The half-life of radium-228 is 6.7 years. After 26.8 years, there would be 7.5 grams of radium-228 remaining from the initial 120-gram sample, which is approximately 6.25% of the original sample.
Step-by-step explanation:
The half-life of radium-228 is 6.7 years. To determine how much of a 120-gram sample of radium-228 would be left after 26.8 years, we can use the formula:
Amount remaining = Initial amount × (1/2)^(t/half-life)
where t is the time period and half-life is the half-life of the substance. Plugging in the values, we have:
Amount remaining = 120 grams × (1/2)^(26.8 years/6.7 years) = 120 grams × (1/2)^4 = 120 grams × (1/16) = 7.5 grams.
Therefore, after 26.8 years, there would be 7.5 grams of radium-228 remaining from the initial 120 gram sample. The fraction of the original sample remaining is 7.5 grams / 120 grams = 0.0625 or 6.25%.