A sample originally contained 2.5 g of rubidium 87 now contains 1.25 g. The half life of rubidium - 87 is 6 x 10 ( to the 10th) years. How old is the sample? Is this possible? why or why not?

See the other post. Same formula.

6 x 10^10 years old b/c it's exactly half of 2.5, Not possible b/c world hasn't existed for 60 trillion years.

To determine the age of the sample, you can use the radioactive decay formula:

N(t) = N₀ * (1/2)^(t / T₁/₂)

Where:
N(t) = final amount of rubidium-87
N₀ = initial amount of rubidium-87
t = time elapsed
T₁/₂ = half-life of rubidium-87 (6 x 10^10 years)

You are given that the initial amount (N₀) is 2.5 g and the final amount (N(t)) is 1.25 g. Substitute these values into the formula:

1.25 g = 2.5 g * (1/2)^(t / (6 x 10^10))

Divide both sides of the equation by 2.5 g to isolate the exponential term:

0.5 = (1/2)^(t / (6 x 10^10))

Take the logarithm of both sides to bring the exponent down:

log(0.5) = log((1/2)^(t / (6 x 10^10)))

Use the logarithmic property to bring the exponent down:

log(0.5) = (t / (6 x 10^10)) * log(1/2)

Now, divide both sides by log(1/2):

log(0.5) / log(1/2) = t / (6 x 10^10)

Multiply both sides by (6 x 10^10):

(6 x 10^10)(log(0.5) / log(1/2)) = t

Evaluate the left side of the equation:

(6 x 10^10)(log(0.5) / log(1/2)) ≈ 9.1 x 10^10

Therefore, the age of the sample is approximately 9.1 x 10^10 years.

Regarding whether this is possible or not, it depends on the context. If the age of the sample is consistent with the formation or event that produced the rubidium-87, then it is possible. However, if the age of the sample contradicts established scientific knowledge or other dating methods, it may indicate a measurement error or other factors affecting the rubidium-87 decay rate.

To calculate the age of the sample, we need to use the concept of radioactive decay and the half-life of rubidium-87.

The half-life of a radioactive substance is the time it takes for half of the substance to decay. In this case, the half-life of rubidium-87 is given as 6 x 10^10 years.

We can use the formula for radioactive decay to determine the number of half-lives that have elapsed:
N = N0 * (1/2)^(t/T)

where N is the final amount, N0 is the initial amount, t is the time passed, and T is the half-life of the substance.

Let's solve the equation using the given information:
N0 = 2.5 g
N = 1.25 g
T = 6 x 10^10 years

1.25 g = 2.5 g * (1/2)^(t/6 x 10^10)

Divide both sides by 2.5 g:
(1/2)^(t/6 x 10^10) = 0.5

To simplify the equation, we can take the logarithm of both sides:
log2((1/2)^(t/6 x 10^10)) = log2(0.5)

Using the logarithm identity for exponents, we get:
(t/6 x 10^10) * log2(1/2) = log2(0.5)

Since log2(1/2) = -1, we can simplify further:
(t/6 x 10^10) * -1 = log2(0.5)

Multiply both sides by -1:
t/6 x 10^10 = log2(0.5)

Now we can solve for t by multiplying both sides by 6 x 10^10:
t = 6 x 10^10 * log2(0.5)

Using the logarithmic property log2(0.5) = log10(0.5) / log10(2), we can get a numerical value for t:
t ≈ 6 x 10^10 * (-0.3010 / 0.3010) ≈ -6 x 10^10

By substituting the value of t back into the equation, we find:
1.25 g = 2.5 g * (1/2)^(-6 x 10^10 / 6 x 10^10)
1.25 g = 2.5 g * (1/2)^(-1)
1.25 g = 2.5 g * 2
1.25 g = 5 g

From the equation, we can see that the final amount (1.25 g) is less than the original amount (2.5 g), which implies that there was not enough time for one half-life to pass. Therefore, it is not possible for the sample to be 6 x 10^10 years old. The sample measurement may have some error or there may have been some other form of loss or decay that has affected the amount of rubidium-87 remaining.