Question

A superhero is rendered powerless when exposed to 40 or more grams of a certain element . A 600 year old rock that originally contained 350 grams of the element was recently stolen from a rock mesuem by the superhero nemesis . The half life of the element is known to be 200 years . How many grams of the element are still contained in the stolen Rock?

Answer 1

To solve this problem, we need to consider the concept of half-life and its application to the decay of the element in question.

Given:
Initial amount of the element in the rock = 350 grams
Half-life of the element = 200 years
Time elapsed since the rock was formed = 600 years

To determine the current amount of the element in the stolen rock, we need to calculate the number of half-lives that have occurred since the rock was formed.

Number of half-lives = Time elapsed / Half-life
Number of half-lives = 600 years / 200 years
Number of half-lives = 3

Since three half-lives have occurred, the original amount of the element has been halved three times.

Remaining amount of the element = Initial amount / (2^(Number of half-lives))
Remaining amount of the element = 350 grams / (2^3)
Remaining amount of the element = 350 grams / 8
Remaining amount of the element = 43.75 grams

Therefore, there are approximately 43.75 grams of the element still contained in the stolen rock.