The isotope samarium-151 decays into europium-151, with a half-life of around 96.6 years. a rock contains 5 grams of samarium-151 when it reaches its closure temperature, and it contains 0.625 grams when it is discovered. the time since the rock reached its closure temperature is years. when the rock was discovered, it had grams of europium-151.

Part A:

The amount of substance left of a radioactive substance with a half life and amount of initial substance is given by



Given that the isotope samarium-151 has a half-life of around 96.6 years and the rock contains 5 grams of samarium-151 when it reaches its closure temperature, and it contains 0.625 grams when it is discovered.

The time since the rock reached its closure temperature is obtained as follows:



Therefore, the time since the rock reached its closure temperature is 289.8 years.

Part B:

Given that the rock contains 5 grams of samarium-151 when it reaches its closure temperature, and it contains 0.625 grams when it is discovered. The number of grams of europium-151 when the rock was discovered is 5 - 0.625 = 4.375

The answer would be $68.04