Final answer:
To calculate the amount of hydrogen left after 19,600 years, we divide the 19,600-year period by the half-life of hydrogen (2,450 years) to get 8 half-lives. Then, we apply the half-life decay by halving the amount of hydrogen 8 times, which leaves us with approximately 11.33 grams of the original 2,900-gram sample.
Step-by-step explanation:
To calculate the remaining amount of hydrogen after a certain number of years, given its half-life, we use the concept of half-life which is the time taken for half of the sample to decay. Since hydrogen has a half-life of 2,450 years, we can find out how many half-lives have passed in 19,600 years, which is 19,600 divided by 2,450 equals 8 half-lives.
Starting with a 2,900-gram sample of hydrogen, we can now calculate the remaining amount:
- After 1 half-life: 1,450 grams remain (half of 2,900)
- After 2 half-lives: 725 grams remain (half of 1,450)
- After 3 half-lives: 362.5 grams remain
- ...Continue this process until 8 half-lives have passed...
After the 8th half-life, the remaining amount of hydrogen is 2,900 / (2^8) grams, which equals approximately 11.33 grams of hydrogen.