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You suspect the bone you found is a fossil and have it tested for the Uranium-235 isotope. The lab informs you that the bone currently has 66% of its original Uranium-235. If the half-life of Uranium-235 is 684 million years, approximately how old is the fossil bone?

a) 1.15 billion years
b) 1.03 billion years
c) 930 million years
d) 800 million years

1 Answer

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Final answer:

The estimated age of the fossil bone with 66% of original Uranium-235 remaining is approximately 400 million years, calculated using the half-life formula and the logarithmic function to solve for time. correct option is not mention.

Step-by-step explanation:

To calculate the age of the fossil bone based on the remaining amount of Uranium-235 (U-235), one can use the concept of half-life, which is the time it takes for half of the radioactive isotope to decay. The half-life of Uranium-235 is given as 684 million years. Since the bone has 66% of its original U-235, it has gone through less than one half-life, as it still has more than 50% of U-235 remaining. The age of the bone can be determined by understanding the relationship between the percentage of Uranium-235 left and the number of half-lives passed.

Starting with 100% of U-235, after one half-life, 50% would remain. This bone has 66%, which means it hasn't completed a full half-life cycle. To find out how much of a half-life has passed, you can use the formula:

original amount × (1/2)^(time/half-life) = remaining amount

This translates to:

1 × (1/2)^(t/684 million years) = 0.66

To find t (the time), you solve for:

(1/2)^(t/684) = 0.66

t = 684 × log0.5(0.66)

Calculate the logarithm:

t = 684 × (-0.585)

t ≈ 400 million years

The bone therefore appears to be approximately 400 million years old, which is not one of the options provided. Thus, a likely error in the options given indicates the need to reassess the question's parameters or the information provided.

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