Question

Scientists estimate Earth's age to be 4.6 billion years. Samarium has a half-life of approximately 106 billion years. From the present date, approximately how many more years must pass before a sample of samarium that was created at the beginning of Earth's history contains 25 percent of the original parent material? 10 billion 26 billion 100 billion 206 billion

Answer 1

1/4 Ao = Ao * ( 1/2)^(t/106)
t = 212
subtract 4.6 billion years
d)

Answer 2

Answer: Option (D)

Explanation: The following steps are shown how decay takes place-

1. Samarium (Sm) initially had 100% of its parent material.
2. Samarium undergoes radioactive decay and becomes half of it i.e 50% of its parent material.
3. To Decay this 50% of its initial material, it takes 106 billion years.
4. Again it undergoes radioactive decay and becomes half of it i.e 25%, and during this process it takes another 106 billion years.

So from the above question, the total number of years for Samarium to contain 25% of its parent material will be (106+106)=212 billion years.

it can also be calculated from the radioactive decay formula.

Thus the most approximate option provided here is option (D).