Tritium, a radioactive isotope of hydrogen, has a half-life of 12.4 years. Of an initial sample of 69 grams, how much will remain after 75 years?

a. 1.5848 grams
b. 61.5289 grams
c. 0.0000 grams
d. 1.0426 grams
e. 17.2500 grams

form the half-life equation,

amount = 69(1/2)^(t/12.4) , where t is in years

plug in 75 for t

show me your work and I will help you with the others.

To solve this problem, we can use the exponential decay formula:

N(t) = N₀ * (1/2)^(t/t₁/₂)

Where:
N(t) is the amount remaining after time t
N₀ is the initial amount
t is the time elapsed
t₁/₂ is the half-life

In this case,
N₀ = 69 grams (initial sample)
t₁/₂ = 12.4 years (half-life)
t = 75 years (time elapsed)

Substituting these values into the equation:

N(75) = 69 * (1/2)^(75/12.4)

Now we can calculate it:

N(75) ≈ 69 * (1/2)^(75/12.4)
N(75) ≈ 69 * 0.095175
N(75) ≈ 6.553725

Therefore, approximately 6.553725 grams will remain after 75 years.

However, none of the answer choices match this value exactly, so let's find the closest option.

The closest option is e. 17.2500 grams, which is not the correct answer. Therefore, none of the given options accurately reflect the amount remaining after 75 years.