The decay constant of radon-222 is $0.181 \mathrm {~d} - 1$. If a sample of radon initially contains $6.00 \times 10 ^ { 8 }$ radon atoms, how many of them are left after $10.0 \mathrm {~d}$ ?

Question

Quizplus · Accepted Answer

The number of atoms remaining after time $t$ is given by:$$N(t) = N_0 e^{-\lambda t}$$where $N_0$ is the initial number of atoms, $\lambda$ is the decay constant, and $t$ is the time.Substituting the given values into the equation, we get:$$N(10 \mathrm {~d}) = (6.00 \times 10^8) e^{-(0.181 \mathrm {~d}^{-1})(10 \mathrm {~d})}$$$$N(10 \mathrm {~d}) = 9.82 \times 10^7$$Therefore, the correct answer is B.

The Decay Constant of Radon-222 Is 0.181 d−10.181 \mathrm {~d} - 10.181 d−1

The Decay Constant of Radon-222 Is $0.181 \mathrm {~d} - 1$