In a recent dig, a human skeleton was unearthed. It was later found that the amount of 14C in it had decayed to (1/rt8) of its original amount. If 14C has a half life of 5760 years,how old was the skeleton?

In a recent dig, a human skeleton was unearthed. It was later found that the amount of 14C in it had decayed to (1/rt8) of its original amount. If 14C has a half life of 5760 years,how old was the skeleton?

8640

To determine the age of the skeleton, we can use the concept of half-life and the given information about the decay of 14C.

First, let's understand the concept of half-life: the half-life of a substance is the amount of time it takes for half of a sample to decay. In this case, the half-life of 14C is given as 5760 years.

Now, according to the question, the amount of 14C in the skeleton has decayed to (1/√8) of its original amount. Mathematically, this can be expressed as:

Amount of 14C remaining = (1/√8) * Amount of 14C initially

Since each half-life reduces the amount of 14C to half, we can rewrite the equation in terms of the number of half-lives:

Number of half-lives = log base 2 (Amount of 14C remaining / Amount of 14C initially)

Now, let's substitute the given values into the equation:

Number of half-lives = log base 2 ((1/√8) / 1)

Next, we can convert this logarithmic equation into exponential form:

2^(Number of half-lives) = (1/√8)

By squaring both sides of the equation, we can eliminate the square root:

2^(2 * Number of half-lives) = 1/8

Since 8 = 2^3, we can rewrite the equation as:

2^(2 * Number of half-lives) = 2^-3

By equating the exponents, we get:

2 * Number of half-lives = -3

Now, solving for the number of half-lives:

Number of half-lives = -3/2

But we know that the number of half-lives cannot be negative. So this means that the amount of 14C remaining can't decayed any further, and thus, the skeleton is approximately:

Age of the skeleton = Number of half-lives * Half-life of 14C

Age of the skeleton = (-3/2) * 5760 years

Therefore, the age of the skeleton is approximately -8640 years. However, since negative years do not make sense in this context, it is likely that there was an error in the given decay information or in the calculations. Please double-check the given information or consult with an expert to determine the correct age of the skeleton.