Final answer:
The percent of the earth's original amount of 40K that remains today is approximately 17.92%.
Step-by-step explanation:
The percent of the earth's original amount of 40K that remains today can be calculated using the concept of half-life. The half-life of 40K is 1.26 billion years, which means that after 1.26 billion years, half of the original amount of 40K will have decayed. In this case, we need to find the number of half-lives that have occurred since the earth was formed, which is 4.5 billion years / 1.26 billion years = 3.57 half-lives.
To calculate the percent remaining, we can use the formula:
Percent remaining = (1/2)number of half-lives * 100
Plugging in the number of half-lives, we get:
Percent remaining = (1/2)3.57 * 100 = 17.92%
After 4.5 billion years, which amounts to approximately 3.57 half-lives of potassium-40 (40K), the percent of 40K remaining can be calculated using the formula: (1/2)n where n is the number of half-lives that have passed. In this case:
(1/2)3.57 = 0.066 or 6.6%
This means that 6.6% of the original amount of 40K remains in the Earth today.