A sample containing 4.0 × 10¹⁸ atoms of a radioactive isotope decays with a half-life of 2.3 years.How many undecayed atoms are left after 3.7 years? A)2.5 × 10¹⁸ B)1.7 × 10¹⁸ C)1.3 × 10¹⁸ D)1.1 × 10¹⁸

Question

Quizplus · Accepted Answer

We can use the formula for radioactive decay:

N = N0 (1/2)^(t/T)

where N0 is the initial number of atoms, N is the final number of atoms, t is the elapsed time, and T is the half-life.

Plugging in the numbers:

N = (4.0 × 10^11) (1/2)^(3.7/2.3)
N = 1.34 × 10^11

So, there are approximately 1.3 × 10^11 undecayed atoms left after 3.7 years.

Therefore, the correct choice is C.

A Sample Containing 4