How long does it take for 25% of the C-14 atoms in a sample of C-14 to decay? answer is 2378

How long does it take for 25% of the C-14 atoms in a sample of C-14 to decay? answer is 2378

The half-life of C-14 is 5730 years.

To figure out how long it takes for 25% of the C-14 atoms to decay, we can use the following formula:

N(t) = N(0) * (1/2)^(t/t_half)

where:

• N(t) is the amount of C-14 remaining after time t
• N(0) is the initial amount of C-14
• t is the time that has passed
• t_half is the half-life of C-14 (5730 years)

We want to find the time (t) when 25% of the C-14 has decayed. So, N(t) = 0.75 * N(0). Plugging this into the formula, we get:

0.75 * N(0) = N(0) * (1/2)^(t/5730)

0.75 = (1/2)^(t/5730)

Taking the natural logarithm of both sides, we get:

ln(0.75) = t/5730 * ln(1/2)

Solving for t, we get:

t = 5730 * ln(0.75) / ln(1/2)

t ≈ 2378 years answer

Therefore, it takes approximately 2378 years for 25% of the C-14 atoms in a sample of C-14 to decay.