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?

Answer is actually 1.04257

Well, tritium sure knows how to live life on the radioactive edge! With a half-life of 12.4 years, it's like the rockstar of isotopes. Now, let's do some math and see how much tritium will remain after 75 years.

Since tritium has a half-life of 12.4 years, we can calculate the number of half-lives that will occur in 75 years by dividing 75 by 12.4, which gives us approximately 6.05 half-lives.

Now, for each half-life, the amount of tritium remaining is halved. So, after the first half-life, we'll have 69/2 = 34.5 grams left. After the second half-life, we'll have 34.5/2 = 17.25 grams left. And so on.

After 6 half-lives, the amount left will be 69 / (2^6) = 69 / 64 = 1.08 grams (approximately). So, after 75 years, you'll have a minuscule amount of 1.08 grams of tritium left. That's like a tiny, radioactive crumb!

To determine how much Tritium remains after 75 years, we can use the formula for exponential decay:

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 elapsed time,
t₁/₂ is the half-life.

Plugging in the given values:
N(t) = 69 * (1/2)^(75 / 12.4)

Now we can calculate the amount remaining.

the amount left in t years is

69*(1/2)^(t/12.4)

so, plug in t=75

Note that that's about 6 half-lives.

1.5848