What is the decay constant for Oxygen-19 if it has a half-life of 26.5s? A)0.0262/s

B)18.4

C)0.0377/s

C)38.2/s

Option A.

Explanation:

We define the half time T as the time such that an initial quantity A reduces to its half.

So we can model the quantity as a function of time like:

P(t) = A*e^(-k*t)

Then for the half time, T, we will have:

P(T) = A/2 = A*e^(-k*T)

solving for k, we get:

A/2 = A*e^(-k*T)

1/2 = e^(-k*T)

ln(1/2) = ln( e^(-k*T)) = -k*T

-ln(1/2)/T = k

Here we know that the half time is T = 26.5s

if we input that in the above equation, we get:

-ln(1/2)/26.5s = k = 0.0262 s^-1

Then the correct option is A