The half-life of the first order radioactive decay of is 1.30 10 9 years. How long would it take for the to decay to 25% of its original concentration?

Question

The half-life of the first order radioactive decay of  is 1.30 10 9 years. How long would it take for the  to decay to 25% of its original concentration?

Quizplus · Accepted Answer

To find the time it takes for the sample to decay to 25% of its original concentration (i.e. 75% has decayed), we need to use the formula for first order radioactive decay:

N/N₀ = e^(-kt)

where N is the final concentration (75% of N₀), N₀ is the initial concentration, k is the decay constant (ln2/t½), and t is the time. Solving for t:

0.75 = e^(-k(1.3×10^9))

ln(0.75) = -k(1.3×10^9)

k = 5.17×10^-10

Now we can use this value of k to find t when N/N₀ = 0.25:

0.25 = e^(-5.17×10^-10 t)

ln(0.25) = -5.17×10^-10 t

t = 2.60×10^19 seconds, or about 8.24×10^11 years. Therefore, the answer is D.

The Half-Life of the First Order Radioactive Decay of