A radioactive element has a half-life of 17 min. How many minutes will it take for the number of atoms present to decay to 1/8th of the initial value?
A) 450 min
B) 51 min
C) 2.1 min
D) 136 min
E) 250 min

Question

Quizplus · Accepted Answer

We can use the formula for radioactive decay:

N(t) = N0 * (1/2)^(t/t1/2)

where:
N(t) = number of atoms present at time t
N0 = initial number of atoms
t1/2 = half-life of the element

We want to find the time it takes for the number of atoms to decay to 1/8th of the initial value, so:

N(t) = N0/8 = N0 * (1/2)^n

where n is the number of half-lives that have passed.
We can solve for n:

(1/8) = (1/2)^n
2^-3 = 2^-n
n = 3

So, 3 half-lives must pass for the number of atoms to decay to 1/8th of the initial value. Since each half-life is 17 minutes:

t = 3 * 17 min = 51 min

Therefore, the answer is B.

A Radioactive Element Has a Half-Life of 17 Min